World Champion Anderson was bidding to take the £30,000 title in the 24-player tournament and delight his home support in Scotland, and began in style by racing into a 3-0 lead against Jenkins.
However, the nine-time major finalist hit 180s in four straight legs as he edged ahead and took out 121 on the bull for a 5-4 lead.
Anderson took out 100 to force a deciding leg, but wasted three match darts as Jenkins escaped from four misses of his own to land double five for the win, silencing the home support.
Jenkins had also defeated Northumberland's Chris Dobey 6-5 earlier in the day, surviving three missed match darts from the TV debutant, but will now compete for the title in Sunday's final day.
"It was tough because you're playing against Gary and the crowd, but he's the local bloke and he deserved the support," said Jenkins.
"It's hard and going 3-0 down didn't help me, but I knew if I could start scoring a bit better than it would make Gary try harder and that's how it proved.
"I put four good legs together and he started struggling, but it was a massive relief to see the winning double go in."
Jenkins will now play Adrian Lewis, August's Auckland Darts Masters champion who defeated World Youth Champion Keegan Brown 6-2.
Brown had hit four ton-plus checkouts in his first round win over Ian White and also took out 132 and 85 on the bull, but was no match for Lewis as the Stoke ace progressed.
World number one Michael van Gerwen's bid to win a third straight TV tournament began with a 6-1 defeat of Scotland's Robert Thornton, the Ayrshire ace who overcame Devon Petersen in round one.
Thornton, though, never recovered from seeing van Gerwen, aided by two 180s and a 177 score, race into a 3-0 lead as the Dutchman sealed victory with a 101 average.
"I'm very happy with this win," said van Gerwen. "I knew what to expect playing Robert in Scotland and it was a good match.
"This has set up for the tournament and I can't wait for Sunday now. Raymond's always a tough opponent and after playing him so many times on the World Series this year it's fitting that we're playing again tomorrow."
Van Gerwen's quarter-final opponent will be Dutch rival Raymond van Barneveld, who defied a 164 finish from Mark Webster to claim a 6-2 win from their second round game.
Phil Taylor, the top seed following three World Series tournament wins in Japan, Perth and Sydney this year, began his challenge to claim the title by sweeping aside Dave Chisnall 6-1.
Chisnall had been in superb form to defeat Kyle Anderson in Saturday afternoon's first round, but never pressured Taylor as the 16-time World Champion cruised through to the last eight.
"My finishing was good but I've got to improve my scoring a bit on Sunday if I'm going to get the job done so I'll knuckle down against Stephen," said Taylor.
"It's an exciting event and I'd love to win, but it's going to be a tough day."
Former Sydney Darts Masters finalist Stephen Bunting defied a bout of illness as he came from 4-2 down to defeat Austria's Rowby-John Rodriguez 6-4 and set up a quarter-final against Taylor.
"It was a really nervy game and I'm just glad to get through it because I didn't sleep much last night and I've not been well for a few days," said Bunting.
"I'll need to bring my A-game on Sunday if I'm going to win and hopefully I'll have a better preparation."
Peter Wright is aiming to claim his first TV title on Sunday following his impressive opening against German teenager Max Hopp, with his 6-3 win earning a clash with James Wade in the last eight.
Wade averaged 103 as he whitewashed Jamie Lewis 6-0 in their second round game, but Wright is confident that he can see off the eight-time major winner before challenging to win his maiden televised tournament.
"It was a tough start," said Wright. "Max is a great young player and I knew I had a tough game against him, but he let me off when he missed a few doubles and I stepped in.
"The crowd got me through it and their support was great, so I didn't want to let them down and I didn't. The welcome when I got out there was fantastic, especially seeing so many people in the crowd dressed up like me.
"That's why I like to give it back to them, to show the appreciation, and it would be wonderful if I can go on and win this now on Sunday.
"That would be amazing but I've got to take one leg at a time because I've got James Wade first and I'll have to play well because James is on form.
"I've played him many times this year already and he's got the advantage, but I think I'm playing a little bit better.
"Jamie Lewis didn't turn up so James didn't have any pressure on him, but he'll have pressure on him when we play because I'll battle all the way."
Wade was in top form as he saw off Wales' Lewis, who had only one dart at a double during the 13-minute contest after producing an impressive display earlier in the day to defeat Dutch youngster Benito van de Pas.
South Africa's flamboyant Devon Petersen had entered the stage against Thornton on a hoverboard, but missed doubles cost him against the Scottish favourite.
Australian pair Simon Whitlock and Kyle Anderson were knocked out by Rodriguez and Chisnall, while Hopp took out 142 and 102 in his win over Belgian debutant Dimitri Van den Bergh.
Webster had impressed with a 100 average as he saw off world number eight Michael Smith 6-4, while Brown was a 6-4 winner against Ian White in a game which featured six ton-plus checkouts.
The £155,000 tournament concludes on Sunday, with the quarter-finals in the afternoon session and the semi-finals and final in the evening session at the Braehead Arena. Tickets are available on the day from the Braehead Arena Box Office.
Unibet World Series of Darts Finals
Saturday November 21
Simon Whitlock 4-6 Rowby-John Rodriguez
Benito van de Pas 4-6 Jamie Lewis
Max Hopp 6-3 Dimitri Van den Bergh
Michael Smith 4-6 Mark Webster
Keegan Brown 6-4 Ian White
Kyle Anderson 4-6 Dave Chisnall
Devon Petersen 3-6 Robert Thornton
Terry Jenkins 6-5 Chris Dobey
Best of 11 legs
Stephen Bunting 6-4 Rowby-John Rodriguez
James Wade 6-0 Jamie Lewis
Peter Wright 6-3 Max Hopp
Raymond van Barneveld 6-2 Mark Webster
Adrian Lewis 6-2 Keegan Brown
Phil Taylor 6-1 Dave Chisnall
Michael van Gerwen 6-1 Robert Thornton
Gary Anderson 5-6 Terry Jenkins
Best of 11 legs
Sunday November 22
Afternoon Session (12.45pm)
James Wade v Peter Wright
Phil Taylor v Stephen Bunting
Adrian Lewis v Terry Jenkins
Raymond van Barneveld v Michael van Gerwen
Best of 19 legs
Evening Session (7pm)
Taylor/Bunting v Wade/Wright
Lewis/Jenkins v van Barneveld/van Gerwen
Best of 21 legs
Best of 21 legs
AFTERNOON SESSION - FIRST ROUND
Simon Whitlock v Rowby-John Rodriguez
0-1 - Whitlock misses tops, allowing Rodriguez in to finish 48.
1-1 - The Australian levels by hitting double ten for a 13-darter.
1-2 - Whitlock misses his chance to break throw, allowing Rodriguez back in on double ten.
1-3 - Rodriguez hits double 16 to break throw and move two legs up with a 14-darter.
2-3 - Two missed doubles from the Austrian allow Whitlock to hit back on double six.
2-4 - Whitlock misses double seven for a 122 finish to level, and Rodriguez finishes 70 on double six to regain his lead.
3-4 - Whitlock fires in a 162 score before hitting tops to respond.
3-5 - Double 16 moves Rodriguez to the brink of victory.
4-5 - Whitlock finishes another 13-darter on double 18 to keep his hopes alive.
4-6 - Whitlock misses the bull to force a deciding leg, and Rodriguez hits double 16 to seal his second round spot against Stephen Bunting.
Benito van de Pas v Jamie Lewis
1-0 - van de Pas lands a 180 before hitting double 16 to claim the opening leg.
1-1 - Lewis hits a 177 score before recovering from five missed doubles to land double eight.
2-1 - The Dutch youngster takes out 112 on tops to regain the edge.
2-2 - Double eight allows Lewis to level.
3-2 - van de Pas takes out 96 to continue his strong finishing.
3-3 - Lewis initially misses the bull to finish 161, but returns on double eight.
4-3 - Lewis misses a dart at tops to break throw, and van de Pas hits the same bed to regain the lead.
4-4 - van de Pas lands a superb 171 score to leave 36, but three misses at double 18 allow Lewis in to hit the bed and avert a possible break of throw.
4-5 - Lewis breaks throw for the first time by taking out 70 on double eight.
4-6 - Double 16 sees Lewis secure the win and a second round spot against James Wade.
Max Hopp v Dimitri Van den Bergh
1-0 - Van den Bergh misses the bull and two darts at double 15, allowing Hopp in on double 16 to lead.
1-1 - Hopp hits a 180, but the Belgian hits double ten to level.
2-1 - A superb 142 checkout, ending on double 11, sees Hopp regain the lead.
3-1 - Hopp breaks throw by taking out 82 on tops, despite Van den Bergh landing a 171 score.
4-1 - Hopp lands another maximum before finishing double eight to win a third straight leg.
4-2 - Hopp misses tops for a 120 checkout, allowing Van den Bergh back in to land double one to respond.
5-2 - Hopp posts a 180 before finishing double ten to move a leg away from the win.
5-3 - Hopp misses four match darts at double 18 and nine, and Van den Bergh steps in on double 16 to stay in the game.
6-3 - The German teenager sets up a second round clash with Peter Wright by taking out 102 on double six.
Michael Smith v Mark Webster
0-1 - Webster fires in a 177 score before finishing double ten to break throw immediately.
1-1 - Webster misses three darts to double his lead, allowing Smith back in on double five to level.
1-2 - The Welsh left-hander moves back ahead with a superb 11-dart finish, scoring 140, 180 and 127 before hitting tops.
1-3 - Smith misses the bull to take out 94, and Webster lands double 12 to move two legs up.
2-3 - Webster hits a 180 but Smith posts a third-dart double five to respond.
2-4 - Webster takes out 52 on tops to regain his two-leg lead.
3-4 - Smith lands a 180 and double 14 to hit back.
3-5 - Smith opens with a 177 and leaves 48 after nine darts as he seeks a break, but Webster takes out a superb 122 on double seven to move to the brink of victory.
4-5 - Smith takes out 58 on tops to keep his hopes alive.
4-6 - Webster hits a timely 180 before finishing 88 for an 11-darter to seal the win and set up a second round clash with Raymond van Barneveld.
Keegan Brown v Ian White
1-0 - Brown finishes 106 to win the game's opening leg.
2-0 - Brown breaks throw with a 105 checkout to double his lead.
2-1 - Tops sees White break throw to claim his first leg.
2-2 - White fires in a 180, and when Brown misses tops, double three sees the Stoke ace level.
3-2 - White lands another maximum, but Brown takes out a brilliant 136 finish to regain the lead with his third ton-plus checkout.
4-2 - White misses double 18 to level, and Brown steps in to break throw on double ten.
4-3 - White checks out a superb 143 finish to hit back.
4-4 - White now finishes 110 as the ton-plus checkouts continue to flow.
5-4 - Brown regains the lead with a superb 150 checkout.
6-4 - Brown opens the leg with a 180, and when White misses double 12 for a 141 checkout, the World Youth Champion hits tops to seal the win, earning him a clash with Adrian Lewis in the second round.
Kyle Anderson v Dave Chisnall
0-1 - Chisnall claims the opening leg to move ahead.
0-2 - Anderson lands a 180 but misses three doubles as Chisnall breaks throw on double three.
0-3 - Double four sees Chisnall move three legs up.
1-3 - Anderson hits another maximum before landing double 15 to claim his first leg.
2-3 - Chisnall misses two darts at double 18, allowing Anderson in to break throw by finishing 64 on double ten.
3-3 - Double 16 sees Anderson level the game.
4-3 - The Australian moves ahead by taking out 80 on double ten to win his fourth straight leg.
4-4 - Anderson lands a 180 but Chisnall finishes 48 on double eight to hit back.
4-5 - Both players post maximums before Chisnall finishes 62 on double 16 to move back ahead.
4-6 - Chisnall adds another maximum, and punishes four missed darts at double top from Anderson to land double 19 for the win, moving through to face Phil Taylor.
Devon Petersen v Robert Thornton
0-1 - Petersen delights the crowd with his unique walk-on, which features a hoverboard, but Thornton wins the opening leg on double two in front of his home crowd.
1-1 - Both players land 180s before Thornton pays for missed doubles as Petersen returns on double eight to level.
2-1 - The pair trade maximums again before Petersen takes out 80 on double ten, after Thornton misses tops for a 106 finish.
2-2 - For a third successive leg both players hit 180s, before Thornton checks out 136 to level.
2-3 - Thornton lands tops to move back ahead.
2-4 - Five missed doubles from Petersen allow Thornton back in to hit a third-dart double top to break throw.
2-5 - Both players initially miss tops for ton-plus finishes before Thornton returns to hit the bed and move a leg away from victory.
3-5 - Petersen lands a 180 before double one keeps his hopes alive.
3-6 - Thornton hits double top to seal the win, setting up a tasty second round clash with Michael van Gerwen.
Terry Jenkins v Chris Dobey
0-1 - Dobey punishes a missed double from Jenkins by taking out 83 to win the opening leg, settling any nerves on his TV debut.
1-1 - Jenkins opens with a 180 before finishing double six to level.
1-2 - Double ten sees Dobey regain the edge.
2-2 - Jenkins levels again by finishing double 18.
3-2 - Dobey misses double 16 to finish 104, and Jenkins checks out 101 on tops for the game's first break of throw.
3-3 - The pair trade 180s before Dobey this time takes out 101 as he levels.
4-3 - Jenkins opens with 180 and 140 before finishing 76 to regain the lead.
4-4 - Five missed doubles from Jenkins are punished as Dobey lands tops to level.
4-5 - Dobey hits a 180 before finishing double 16 to move back in front.
5-5 - Dobey misses double 12 and six to claim victory with an 81 finish, and Jenkins hits double eight to send the match into a decider.
6-5 - Dobey is unable to take out 110, and Jenkins posts tops to edge to victory, moving him through to face World Champion Gary Anderson.
EVENING SESSION - SECOND ROUND
Stephen Bunting v Rowby-John Rodriguez
0-1 - Rodriguez lands the game's first 180, and punishes six missed doubles from Bunting to win the opening leg on double two.
1-1 - Bunting hits a maximum and tops to level.
1-2 - Another leg sees both players miss doubles across two visits before Rodriguez again lands double two to edge ahead again.
1-3 - Rodriguez lands two 180s before finishing double three to move two legs clear.
2-3 - Bunting this time hits double three as he responds.
2-4 - Bunting lands two 180s before Rodriguez lands a 177 to leave 28, and when the English ace misses the bull to finish 81 the Austrian takes out double 14 to regain his cushion.
3-4 - Both players land maximums before a miss at tops from Rodriguez allows Bunting in on double eight.
4-4 - Double 16 sees Bunting level.
5-4 - Rodriguez misses tops for a 107 finish, and Bunting hits double six to lead for the first time.
6-4 - Bunting hits his fifth 180 before landing double 16 to complete the fightback.
James Wade v Jamie Lewis
1-0 - Wade breaks throw immediately by taking out 40.
2-0 - A 14-dart leg sees Wade double his advantage.
3-0 - Lewis misses a dart at tops to finish 80 before Wade hits the same bed for a 13-darter.
4-0 - Wade wins his fourth straight leg as he takes out 40 for another 14-darter.
5-0 - Wade lands a 180 and takes out 86 for another break of throw.
6-0 - Tops sees Wade complete the whitewash victory with a 103.66 average.
Peter Wright v Max Hopp
0-1 - Double ten sees Hopp claim an immediate break of throw.
1-1 - Wright hits a 180 and lands tops to level, after Hopp misses double ten for a 100 finish.
2-1 - The pair trade 180s before Wright lands double six to lead,
3-1 - Hopp misses three darts at double top and ten, allowing Wright in on tops to break.
4-1 - Double eight sees Wright claim his fourth straight leg.
4-2 - Hopp lands double ten to hit back, after Wright misses a dart at tops.
4-3 - Wright is unable to hit double 16 to finish 110, and Hopp lands double two as he breaks throw.
5-3 - Hopp misses two darts to level, at double 14 and seven to finish 88, as Wright steps in on tops to move a leg away from the win.
6-3 - Hopp lands a 180, but Wright lands tops as he secures his spot in the quarter-finals against James Wade.
Raymond van Barneveld v Mark Webster
1-0 - Double ten for a 60 finish sees van Barneveld claim the opening leg.
2-0 - van Barneveld lands a 180 and double six to move two legs up.
3-0 - van Barneveld's fine start continues as he takes out 78 on double six.
4-0 - The Dutchman lands a 180 and double seven to claim a fourth straight leg.
5-0 - van Barneveld takes out 114 to move a leg away from victory.
5-1 - Webster hits a 180 and finishes a brilliant 164 to save the game.
5-2 - Webster initially misses tops for a 160 finish before returning on double ten.
6-2 - van Barneveld hits tops to claim the win and move through to the quarter-finals.
Adrian Lewis v Keegan Brown
1-0 - Brown's 180 is countered by a 177 from Lewis, who wins the leg on double one.
2-0 - Lewis takes out 88 on the bull to double his lead.
2-1 - Lewis this time misses the bull for an 88 checkout, and Brown finishes 85 on the middle double to break throw and get off the mark.
3-1 - Lewis takes out 66 on double 18 to move two legs clear.
4-1 - Lewis initially misses two darts to win the leg before posting double one, for the second time, to open up a three-leg lead.
4-2 - Brown finishes a superb 132 checkout with two bullseyes and double 16.
5-2 - Lewis fires in a 180 and double 14 to move a leg away from the win.
6-2 - Brown misses four darts at doubles to stay in the game, and Lewis finishes double eight for the win.
Phil Taylor v Dave Chisnall
1-0 - Chisnall fires in the game's first 180, but Taylor lands tops for a 13-darter.
1-1 - Chisnall finishes 81 on double six to level the game.
2-1 - Double three sees Taylor regain the lead.
3-1 - Chisnall lands a 180 but double 16 sees Taylor break throw.
4-1 - Double ten sees Taylor claim a third straight leg.
5-1 - Chisnall misses double 12 to hit back, and Taylor returns on double one as he moves a leg away from the win.
6-1 - Taylor seals victory with double 18 as he moves through to meet Stephen Bunting in the quarter-finals.
Michael van Gerwen v Robert Thornton
1-0 - van Gerwen lands scores of 177 and 180 as he takes the game's opening leg.
2-0 - The world number one adds another 180 before recovering from five missed doubles to punish Thornton for four wasted chances by landing double four to break throw.
3-0 - Double 18 gives van Gerwen a third successive leg.
3-1 - Thornton lands a 180 and double ten to claim his first leg.
4-1 - van Gerwen lands two maximums in the leg before finishing double ten to regain his cushion.
5-1 - Thornton misses double top for a 160 finish, and van Gerwen capitalises to move to the brink of victory.
6-1 - Thornton hits a 180, but van Gerwen finishes 64 on double eight to complete the win and set up an all-Dutch quarter-final with Raymond van Barneveld.
Gary Anderson v Terry Jenkins
1-0 - Jenkins is punished for two missed doubles as Anderson hits tops for an immediate break.
2-0 - Tops sees the World Champion double his lead, to the delight of the home crowd.
3-0 - Anderson capitalises on another miss from Jenkins by finishing 62.
3-1 - Jenkins fires in a 180 before punishing Anderson for four missed doubles by hitting double six.
3-2 - Jenkins opens with a 180 before landing double ten to reduce the gap to one leg.
3-3 - Jenkins posts a maximum for a third successive leg before punishing Anderson's miss at tops by hitting the same bed to level.
3-4 - The nine-time major finalist's charge continues as he trades 180s with Anderson before landing tops to move ahead for the first time.
4-4 - Double top sees Anderson hit back to win his first leg in five.
4-5 - Jenkins takes out 121 on the bull to move back in front and to the brink of the win.
5-5 - Anderson finishes 100 on double 19 to send the game into a decider.
5-6 - Jenkins is first to a finish before Anderson lands a 180 - but the Scot is unable to capitalise on four misses from his opponent when he sees three match darts slip away, allowing Jenkins back in on double five to edge the win.