The clash between the reigning World Champion and the 16-time World Champion was billed as the highlight of the opening day at the Butlins Minehead Resort, with the pair's ProTour rankings this year meaning that they clashed in round one.
Taylor would miss double 12 for a nine-darter during a thrilling contest and led 4-3, but Anderson won three of the final four legs as he progressed to face Daryl Gurney.
After trading 13-darters in the opening two legs, the duo then swapped 11-dart legs in an opening of stunning quality, with Anderson's 180s in legs one and three being followed by eight perfect darts from Taylor in the fourth as he missed double 12 to complete a perfect nine-darter.
Anderson then received a let-off for five missed doubles in the fifth as Taylor was off-target with two darts at double eight, allowing the Scot to return on double six.
Taylor then levelled with the aid of a 180 in leg six before breaking throw for the first time in the next, with Anderson wiring double 19 to check out 115 before the three-time Players Champion took out a stunning 148 finish.
Three missed doubles from Taylor in leg eight then allowed Anderson to level on tops before a 13-darter put the Scot a leg away from victory - but the Stoke legend levelled on double two to force a decider.
Anderson, though, hit two timely 180s in the final leg before landing double ten to complete a 14-darter for the win, setting up a second round meeting with Northern Ireland's Daryl Gurney.
"The two 180s were huge for me in that final leg and pulled me out of the fire," admitted Anderson. "I'm always happy to get over the finishing line, especially against Phil. His 148 hurt but I had to stick with him.
"It gets harder from here - there's a jinx going about that if you beat Phil then you go out in the next game or you don't go on to win the tournament, so hopefully that's wrong!
"I've got Daryl next and he played well. He'll be up for it because he's here to win, just like everyone else."
Gurney had earlier impressed on his debut in the event, as he overcame 2012 finalist Kim Huybrechts 6-2.
Although Huybrechts - the number five seed - opened the game with a 12-darter, Gurney levelled with a 120 checkout, hit two 180s in an 11-darter and then double eight for a 14-dart leg for a 3-1 lead.
Huybrechts hit seven perfect darts to open the fifth leg, but missed three darts at double 16 to allow Gurney in on double eight, before a 72 checkout moved the Northern Irish ace 5-1 up.
Double eight saw Huybrechts respond, but Gurney finished double four in the next to complete a strong performance as he reached the last 16 of a PDC major for the first time.
"I've been practising really hard so I'm happy to get the win there," said Gurney.
"Every game on TV is a little bit more experience and it's looking a little bit better than it was 12 months ago. I'm trying to be more dedicated and put more hours in because the players in the PDC are ruthless."
Michael van Gerwen overcame a scare against World Youth Champion Keegan Brown before moving through to the second round with a 6-4 win to kick off his bid to win a fourth successive TV event.
The world number one and top seed was fully tested as Brown led twice during a see-saw contest, although Brown ultimately paid for missed doubles in the last two legs.
Double eight gave Brown the opener before van Gerwen, following two 180s, hit the same double to take the next two legs for a 2-1 lead.
Van Gerwen also landed a 174 in leg four, but Brown's 180 set up double 18 as he levelled before the Isle of Wight ace landed a maximum and tops or a 3-2 lead.
Van Gerwen responded with a maximum and double six to level, before Brown's miss allowed him in on tops to break throw for a 4-3 lead.
Brown hit a 180 and double six to level, but missed double 18 in the ninth leg as van Gerwen edged 5-4 up, before his missed bull allowed the Dutchman in on double four to set up a second round meeting with Vincent van der Voort.
"I'm really glad that I won in the end," said van Gerwen. "He finished really well at the beginning of the game and I was struggling, but there was also a lot of pressure on me and I tried to get into the game.
"I can do a lot better but I'm through to the next round and it's a longer format and I feel more comfortable with that."
Van der Voort punished missed doubles from Justin Pipe as the two-time Minehead semi-finalist lost out 6-1 in their first round battle.
After van der Voort took the opener, with the aid of a 180, Pipe broke back on double 16 but was unable to capitalise on a maximum of his own in the third as he missed five darts at doubles to allow the Dutchman in on tops.
Pipe missed one further double in the next two legs as van der Voort moved 4-1 up, with the Dutchman then finishing 157 to continue his charge before swapping 180s with his opponent in leg seven before taking out 87 for victory.
Number two seed Michael Smith made a strong start to his bid for glory at the Players Championship Finals with a 6-3 win over Jamie Caven on Friday afternoon.
Smith has won two European Tour events and a UK Open Qualifier this year in his rise into the world's top ten, and was in confident mood to secure a second round tie with Mensur Suljovic.
Although Caven hit back from 2-0 down to level, the Derby ace was punished for missed doubles in the next two as Smith, aided by a 92 checkout, pulled clear to lead 5-2 before holding out to take the win with six doubles from 13 attempts.
Austrian ace Suljovic was in strong finishing form as he defeated Mervyn King 6-1, with the Norfolk ace battling against sciatica as his bid to reach the final for a second time was ended in the opening round.
Suljovic, though, showed no mercy with early checkouts of 116 and 89 - for a 12-dart leg - before double ten gave him a third successive leg.
King hit back on double eight, but Suljovic regained his cushion on double 16 before hitting a pair of double ten checkouts to seal the win.
Peter Wright punished Steve Beaton's missed doubles as the number three seed moved into the second round with a classy 6-2 victory, hitting six doubles from 13 attempts in his win.
Beaton missed a total of five doubles in the opening four legs as Wright, aided by a 112 finish, took command, and a 76 checkout saw the Scot take a five-leg cushion.
Beaton found his range with a sublime 132 finish of bullseye, treble 14 and tops, and he also claimed a second leg to continue his revival, but Wright landed a 180 in the next leg before punishing a missed bull from his opponent with an 80 finish to complete the win.
Wright now takes on Simon Whitlock, who capitalised on 19 missed doubles from Brendan Dolan as the Australian claimed a 6-2 victory with 50 percent on his own doubles as he moved through to the last 16.
After winning the opener on double ten, Whitlock then stepped in to punish Dolan for nine missed doubles in leg two and a further four misses in the third as he opened up a 3-0 lead.
Dolan responded on double six and double eight to win two of the next three, but four more misses allowed Whitlock in on double 16 for a 5-2 lead before the former European Champion hit a 180 and finished 80 for the win.
James Wade won the battle of the left-handers with Mark Webster as a 6-3 victory sees him progress to face Benito van de Pas on Saturday.
Wade kicked off the match with a 180 before finishing double ten for a 12-darter before another pair of double ten finishes - punishing seven misses from Webster across two legs - saw him take a 3-0 lead.
Webster finished 55 to hit back in leg four, but Wade landed a 180 and tops for a 4-1 lead before landing seven perfect darts in a 12-dart finish to move four legs clear of his rival.
Webster punished missed bullseyes from his opponent to win the next two, taking out 93 for a 14-darter and double ten, as he battled back, but Wade sealed his win with a superb 102 checkout.
Van de Pas, meanwhile, held off Stephen Bunting's fightback from 5-0 down before he edged through to the last 32 with a 6-4 defeat of the former Lakeside Champion.
The Dutch youngster was in fine finishing form as he took out 96, 90 and tops - following a 180 - to lead 3-0, and checkouts of tops and double 16 to move to the brink of victory.
Bunting fired his challenge with a 180 as he took leg six, before finishing 84 on the bull, double eight and double 16 to reduce the gap to 5-4 - but he crucially missed five dart at doubles to level as van de Pas stepped in with a 70 finish for victory.
Gerwyn Price impressed on his Players Championship Finals debut by coming from 3-1 down to defeat Jelle Klaasen 6-4.
After the Welsh ace finished 97 in the opening leg, Klaasen levelled with a 112 checkout and then took out a brace of double nine finishes to move two legs clear.
A missed bullseye in the fifth leg allowed Price to follow a 180 with tops to respond, before he took out 96, tops and 116 to move 5-3 up, and though Klaasen replied on double 18, the Welshman landed another 96 checkout to seal the win.
Price now faces Ian White, who edged through with a narrow 6-5 defeat of Raymond van Barneveld in their opener at Butlins Minehead, in a tight clash where there was never more than one leg between the pair.
After an 81 finish saw van Barneveld take the opener, White hit tops and double eight for a 2-1 lead before the Dutchman took out a superb 141 checkout to level.
Van Barneveld then opened the fifth leg with two 180s to set up the possibility of a nine-darter, but after missing out this time on the 141 checkout he missed five doubles before White stepped in to take out 68 and move 3-2 up.
The next five legs also went with throw to send the game into a decider - with van Barneveld taking out 126 in the eighth and punishing two missed match darts from his rival in the tenth - but White was first to a finish as he checked out 68 to sneak the win.
Dave Chisnall banished his Minehead blues with a superb 6-0 whitewash of Joe Murnan, limiting the debutant to just three darts at a double in the contest.
Chisnall, who had lost in the first round of the Players Championship Finals for three successive years, made a confident start with a 171 in the opening leg and a 180 in a 13-darter to move 2-0 up.
He added double four and tops to lead 4-0 before Murnan was unable to land double 12, six and three in the fifth leg, as Chisnall stepped in on double 19 to continue his charge before double five secured a whitewash.
Chisnall now plays Jamie Lewis, who produced one of the finest performances of his emerging career as he landed six 180s before edging out Robert Thornton 6-5 in an 11-leg thriller.
Lewis hit a maximum in each of the game's opening five legs, although a 14-darter gave Thornton an early 2-1 lead before the Welsh thrower penalised a miss from his opponent in the fourth and took out 101 to move ahead at 3-2.
Thornton took out a superb 138 checkout to level, before Lewis followed another maximum with double 16 to regain the edge with a 4-3 cushion.
Timely 180s from the Scot helped him to win the next two to regain the edge at 5-4, but a miss at double 16 for a 112 finish in leg ten allowed Lewis to finish 96 to force a decider which the youngster took on double 12.
Adrian Lewis held off John Henderson's gallant challenge to move through to a second round clash with Alan Norris courtesy of a 6-3 comeback triumph.
After Lewis made the stronger start, taking out double four and 121, on the bull, to win the opening two legs, the Scot hit back with two double top checkouts to level before following his second 180 with a superb 137 checkout to lead 3-2.
Lewis, though, hit back with a 104 checkout and then hit a 180 and double three to regain the edge at 4-3 before winning a key eighth leg - after Henderson missed a single two to leave tops - with a 66 finish to move clear and double 16 for the win.
Norris enjoyed a winning debut in the Players Championship Finals as he defeated Terry Jenkins 6-3, pulling clear in the second half of the game for victory.
After Norris took the opening leg on double four, Jenkins landed a 180 before levelling in the second after four misses from his rival, before moving 2-1 up after a further three missed doubles in the next leg.
Jenkins then missed his chance to open up a two-leg lead as Norris levelled before the Somerset-born thrower took out 71 and 86 for a 4-2 lead.
Norris then landed two 180s in leg seven, only to miss four darts at doubles as Jenkins stepped in, but the nine-time major finalist replied with an 82 finish for a 5-2 lead before tops secured his second round place.
Saturday's second round at the Butlins Minehead Resort is followed on Sunday by the quarter-finals in the afternoon session and the semi-finals and final in the evening session.
Cash Converters Players Championship Finals
Friday November 27
Justin Pipe (16) 1-6 Vincent van der Voort (17)
Terry Jenkins (11) 3-6 Alan Norris (22)
Jelle Klaasen (10) 4-6 Gerwyn Price (23)
Benito van de Pas (13) 6-4 Stephen Bunting (20)
Mensur Suljovic (15) 6-1 Mervyn King (18)
Brendan Dolan (14) 2-6 Simon Whitlock (19)
Michael Smith (2) 6-3 Jamie Caven (31)
Kim Huybrechts (5) 2-6 Daryl Gurney (28)
Dave Chisnall (8) 6-0 Joe Murnan (25)
James Wade (4) 6-3 Mark Webster (29)
Adrian Lewis (6) 6-3 John Henderson (27)
Robert Thornton (9) 5-6 Jamie Lewis (24)
Michael van Gerwen (1) 6-4 Keegan Brown (32)
Gary Anderson (12) 6-5 Phil Taylor (21)
Ian White (7) 6-5 Raymond van Barneveld (26)
Peter Wright (3) 6-2 Steve Beaton (30)
Saturday November 28
Afternoon Session (12.45pm-5pm)
Michael Smith v Mensur Suljovic
Adrian Lewis v Alan Norris
James Wade v Benito van de Pas
Dave Chisnall v Jamie Lewis
Evening Session (7pm-11pm)
Ian White v Gerwyn Price
Peter Wright v Simon Whitlock
Daryl Gurney v Gary Anderson
Michael van Gerwen v Vincent van der Voort
All games are the best of 19 legs
Titanbet.co.uk Outright Odds
5/4 Michael van Gerwen
9/2 Gary Anderson
7/1 Adrian Lewis, Peter Wright
14/1 Michael Smith
16/1 James Wade, Ian White
20/1 Dave Chisnall
25/1 Mensur Suljovic
40/1 Simon Whitlock
50/1 Gerwyn Price, Alan Norris
125/1 Vincent van der Voort, Benito van de Pas
150/1 Jamie Lewis, Daryl Gurney
Odds correct following First Round, and subject to fluctuation. For latest odds, visit www.titanbet.co.uk.