In an opening night of superb quality in the World Series of Darts event, three players - Anderson, Peter Wright and van Barneveld - all hit six perfect darts in their bid to win the Mercedes-Benz CLK-250 car which sponsors Sixt have offered for a nine-dart finish.
Anderson also landed a maximum 170 checkout before sealing his win over James Wade with a 147 finish, while Stephen Bunting hit a superb 11 maximums only to be edged out 10-9 by Lewis.
And defending champion van Gerwen had to dig deep to come from 4-1 down to defeat Dutch rival van Barneveld 10-8 in another outstanding contest, with the world number one ending the game - held in the unique outdoor arena at the Dubai Duty Free Tennis Stadium - with an average of 106.80.
Van Barneveld was at his clinical best in the early stages as he opened up a three-leg lead and he also set up a possible nine-darter in the game's second leg only to miss out on a seventh perfect dart and then see van Gerwen take the leg.
The world number one hit back strongly in the middle of the game as he levelled with legs of 11, 11 and 13 darts before responding to a 96 finish from van Barneveld with a 14-darter to square the game at five-all.
Van Barneveld then took two of the next three to regain a slender cushion at 7-6, only for van Gerwen to find an extra gear once again, following another 11-darter with a 127 checkout to break and lead for the first time at 8-7.
Van Barneveld landed an 11-darter of his own to break back and level, but van Gerwen took out a key 81 to break and move 9-8 up before hitting his eighth 180 of the contest as he sealed victory in the next leg.
"It means a lot to me and I want to win this title again so much," said van Gerwen, who now plays Lewis in Friday's semi-finals. "The semi-finals will be cracking and I can't look too far ahead.
"I knew that I was playing well tonight and my confidence was there but when I had the chance to hurt him I didn't take it, and Raymond did it at the right times.
"I made mistakes and you can't afford to make mistakes in this tournament because it's really hard to win - it's difficult enough with the heat and the conditions, but I'm through to the next round."
Lewis produced what he described as one of his best-ever performances as he defied 11 maximums from Bunting to edge a 10-9 victory, averaging 105.68 and hitting five 180s and a 174 in reply to his heavy-scoring opponent.
The lead would change hands five times during a thrilling contest, with Lewis landing a 12-darter and a 101 finish early on and Bunting checking out 102 to level and a 12-dart leg of his own to lead 6-5.
Lewis hit an 11-darter as he regained the lead, but Bunting would move 9-7 up with a run of three successive legs - only to be punished for missing three match darts as the world number four levelled and then hit a 180 and double eight in the game's deciding leg.
"I thought it was a brilliant game," said Lewis. "It was tough but under the circumstances it's one of the best wins I've ever had.
"Stephen showed what a quality player he is and that he deserves to be here, and I tried my best to hang in there and match him. It's a massive step in the right direction for me and I'm very proud to get up there and play like that tonight."
World Champion Gary Anderson was also in brilliant form as he claimed a 10-8 win over James Wade, who played his part in a high-quality contest and led 8-7 at one stage before the Scot surged to victory on his World Series of Darts debut.
Anderson had finished 100 to take a 2-1 lead early on, and after Wade finished 128 as he edged ahead it was the new Premier League champion who then took out the maximum 170 checkout to level in leg six.
Wade landed a pair of 12-dart finishes as the next eight legs all went with throw, and after he edged 8-7 up Anderson then took out another 100 finish, for an 11-dart leg, as he levelled.
The Scot then claimed a crucial break of throw by landing his ninth 180 of the game and double five to move 9-8 up, before checking out 147 in the next leg to seal the win.
"Everything's a new experience out here and I had no hopes going into the game, so it was good and I enjoyed it," said Anderson.
"James has been playing well for the last year and if you give him a shot he takes it out - but I've turned into that player myself and if you give me a sniff of it I'll have a shot.
"I played well on my own throw and but James had the advantage of throw and I knew that if I got a chance I had to take it, and I went 9-8 up and then took the 147 out.
"It would be nice to go on and win this now, especially with it being my first time here."
Anderson now plays Taylor in a repeat of January's World Championship final as they clash in the semi-finals on Friday evening - after the 16-time World Champion picked up his first win in Dubai.
Taylor had been defeated by Andy Hamilton and Peter Wright in the quarter-finals in the past two years, but gained revenge against the latter with a fine 10-5 victory.
The pair shared the game's opening eight legs - including an 11-dart finish from Wright and his attempt at a nine-darter which saw him land two 180s - but Taylor pulled clear with five straight legs which included a ten-dart finish and a pair of maximums in another leg.
Wright took out 100 to keep his hopes alive at 9-5, but Taylor fired in another 180 in the next before double 16 sealed his spot in day two.
"It means everything to get the win because it's a tournament that I've never won and that I want to win," said Taylor. "I was pleased to finish Peter off there and I'm over the moon.
"I love Dubai but it's one of the places that I've not done so well in my darts so hopefully I can go through and win it now.
"Peter missed a couple of doubles in the middle of the game but once his back was against the wall he came out fighting and he's one of those players who can come back at you.
"I'm through and I'll take that - but I've got to have my head on against Gary. He's the favourite and it will be a good game, and both semi-finals will be crackers."
The $175,000 tournament concludes on Friday at the Dubai Duty Free Tennis Stadium with the semi-finals and final, where the third Dubai Duty Free Masters champion will be crowned.
Tickets for the Dubai Duty Free Darts Masters are still available, with General Admission tickets and VIP Hospitality tickets on sale. For further information visitwww.dubai-darts.com/tickets , and in person on the day at The Irish Village.
Worldwide television coverage of the tournament will include live broadcasts on Dubai Sports TV and OSN, as well as worldwide through the PDC's series of broadcast parters:
Dubai Sports TV
OSN - Middle East & North Africa
ITV4 - UK (Delayed)
Setanta - Ireland
Fox Sports - Australia
Sky - New Zealand
RTL7 - Netherlands
www.LIVEPDC.TV for International Pass Subscribers outside of UK, Ireland & Netherlands.
Dubai Duty Free Darts Masters
Thursday May 28
Adrian Lewis 10-9 Stephen Bunting
Gary Anderson 10-8 James Wade
Phil Taylor 10-5 Peter Wright
Michael van Gerwen 10-8 Raymond van Barneveld
Friday May 29 (8pm local time)
Phil Taylor v Gary Anderson
Michael van Gerwen v Adrian Lewis
Best of 21 legs
van Gerwen/Lewis v Taylor/Anderson
Best of 21 legs
Adrian Lewis v Stephen Bunting
0-1 - Bunting fires in a nerve-settling 180 before taking out 51 on double 16 to win the opener.
1-1 - Lewis replies with a maximum before taking out 85 on tops for a 12-darter.
2-1 - Lewis finishes 65 on double 12 to move ahead.
2-2 - Bunting hits back immediately, landing a 180 and taking out 76.
3-2 - The pair trade maximums before Lewis finishes 101 to move back in front.
3-3 - Bunting posts a 180 and double six to level.
4-3 - Bunting fires in another maximum but Lewis takes out 84 on double 12 to regain the edge.
4-4 - The high scoring continues as both players land 180s before Bunting finishes 102 on double 16.
5-4 - Double 14 moves Lewis back in front.
5-5 - Lewis misses a dart at tops - only his second miss of the game - to allow Bunting in on double four to level.
5-6 - Bunting breaks with a superb 12-dart leg, featuring his seventh 180 of the game and double ten.
6-6 - Lewis replies in brilliant fashion with an 11-darter, taking out 86.
7-6 - Bunting lands his eighth maximum of the game, but Lewis fires in a 174 score before hitting tops to regain the lead.
7-7 - Bunting lands double ten with his third dart as he squares the contest.
7-8 - Bunting hits another 180, and when Lewis misses three darts at double 18 and nine the St Helens ace steps in to take out 65 on tops.
7-9 - Bunting posts his tenth 180 and then adds double 16 to move a leg away from victory.
8-9 - Lewis keeps his hopes alive by hitting a fourth maximum of the game.
9-9 - Bunting lands yet another maximum, only to miss three match darts - at the bull, double eight and double four - to allow Lewis in on double eight to send the game into a deciding final leg.
10-9 - Lewis hits his fifth 180 before snatching victory on double eight to end a game of superb quality, ending with an average of 105.68.
Gary Anderson v James Wade
0-1 - Wade finishes tops to win the game's opening leg and hold throw.
1-1 - Anderson finishes 60 on double ten to level.
2-1 - The World Champion takes out 100 on tops to break throw and move ahead.
2-2 - Wade checks out a brilliant 128 finish on double ten to hit back immediately.
2-3 - The left-hander regains the lead by finishing 76 on double eight.
3-3 - Anderson levels by taking out the maximum checkout of 170 to delight the Dubai crowd.
3-4 - Anderson lands six perfect darts as he opens with two 180s, but is unable to complete a nine-darter and then sees Wade - who added a maximum of his own - take out tops for a superb 12-dart leg.
4-4 - The pair trade 180s only for Anderson to then miss four doubles to win the leg - but Wade misses tops to punish his rival as the Scot returns on double one.
4-5 - For a third successive leg, an Anderson 180 is followed by a maximum from Wade, who takes out 41 for a 12-darter to move back in front.
5-5 - A 171 score helps Anderson to be first to a finish, and he eventually posts double six to level the game again.
5-6 - Tops sees Wade edge back ahead.
6-6 - Anderson hits his sixth 180 and levels with double ten.
6-7 - Wade returns to land double eight as he regains the edge.
7-7 - Wade misses one dart to break throw for a two-leg lead, at tops, and Anderson hits the same bed to respond.
7-8 - The duo trade 180s before Wade pins tops this time as he moves two legs away from the win.
8-8 - Anderson hits his eighth 180 before finishing 100 for an 11-dart leg.
9-8 - The World Champion lands another maximum before breaking throw with double five as he moves ahead for the first time since leg three.
10-8 - Anderson seals victory in brilliant style with a 147 checkout.
Phil Taylor v Peter Wright
0-1 - Wright breaks throw by taking out 16, punishing a miss from Taylor.
1-1 - Wright misses three darts at double 16, allowing Taylor in to land double 15 to level.
2-1 - Taylor fires in the game's first 180 before taking out double eight to move ahead.
2-2 - Wright lands tops for a 14-darter to level.
3-2 - Taylor takes out 87 to move back in front with a 14-dart finish of his own.
3-3 - Wright hits six perfect darts by opening with two 180s, but like Gary Anderson earlier in the night he is unable to finish 141 - although he returns to finish a 12-darter.
4-3 - Taylor regains the lead with a hold of throw.
4-4 - Wright fires in two 180s in the leg as an 11-darter squares the contest.
5-4 - Double 14 sees Taylor move back in front.
6-4 - Taylor breaks throw with a superb leg as double 16 gives him a two-leg cushion.
7-4 - Taylor finishes 57 on tops to take a third successive leg.
8-4 - Taylor breaks once more with a brilliant ten-dart finish, hitting two 180s and double two.
9-4 - Taylor misses four darts at double 19 to win the leg, but Wright is unable to land five darts at doubles as he allows the world number two back in to move one leg away from victory.
9-5 - Wright wins his first leg in six as he takes out 100 to keep his hopes alive.
10-5 - Taylor lands double 16 to secure victory for the first time in the Dubai Duty Free Darts Masters.
Michael van Gerwen v Raymond van Barneveld
0-1 - The pair trade 180s before van Gerwen misses the bull to break with a 121 finish, allowing van Barneveld to finish tops for a 13-darter.
1-1 - van Barneveld opens with two 180s to set up a possible nine-darter, but misses a seventh treble 20 before going on to lose the leg when van Gerwen finishes double four.
1-2 - van Barneveld lands double ten to regain the lead.
1-3 - The five-time World Champion breaks throw with a clinical two-dart 89 finish to move two legs clear.
1-4 - Double 16 helps van Barneveld to win a third successive leg.
2-4 - van Gerwen hits back with a brilliant 11-darter.
3-4 - The world number one powers in another 11-dart finish as he breaks throw to reduce the gap to one leg.
4-4 - van Gerwen levels the game by posting double ten for a 13-dart leg - meaning he has taken three legs in 35 darts.
4-5 - van Barneveld hits back by finishing 96 in two darts.
5-5 - van Gerwen opens with a 180 before completing a 14-darter to level again.
5-6 - For the first time in the game both players are unable to land their doubles, with four misses from van Gerwen allowing van Barneveld back in following five misses to land double two to regain the edge.
6-6 - Double ten sees van Gerwen respond in style.
6-7 - van Gerwen misses double 11 for a 142 finish, and van Barneveld averts a possible break on double eight.
7-7 - van Gerwen levels with another 11-dart finish.
8-7 - van Gerwen breaks by finishing 127 on double eight for a 12-darter.
8-8 - The pair trade 180s as van Barneveld breaks back with a superb 11-dart finish of his own.
9-8 - Another leg goes against the throw as van Gerwen finishes 81 for a 14-darter.
10-8 - van Gerwen opens the leg with a 180 before completing victory to retain his unbeaten record in the history of the Dubai Duty Free Darts Masters.