Taylor had travelled to Dublin aiming to win the double-start tournament for a 12th time since 1998, but saw his hopes dashed at the Citywest Hotel in Dublin as he lost in straight sets - despite missing the bullseye for a nine-dart finish!
Taylor's narrow miss for a perfect leg came in the game's second leg, which he won in 14 darts, but he found himself 2-1 down as van der Voort punished missed doubles in the other two legs.
An 81 checkout for Taylor levelled the set, but van der Voort opened the decider with a 160 score - as his rival missed his first three opening doubles - before finishing double two to claim the lead.
A high-scoring second set saw the first four legs go with throw - despite van der Voort landing a 180 in each - as Taylor sought to level, but the deciding leg saw him miss double 16 for a 105 finish to allow the Dutchman in on double eight to claim a momentous win.
"Phil's the best player every and everything around him is magical," said van der Voort. "To beat him here is an amazing feeling.
"I was very focused and determined to win today and I'm glad I pulled it off. My finishing helped me - I can score as well as anybody but my finishing sometimes lets me down, and today it didn't so I'm really happy.
"I've got a day off now and I've got to realise that the next match is just as important as this."
World number six James Wade, the 2007 and 2010 winner, was also eliminated as Austrian ace Mensur Suljovic came from a set down to win 2-1 with six straight legs in a high-quality clash.
Wade took out 118 as he claimed the first set 3-1 and also led 1-0 in the second before a superb response from Suljovic saw him take the next three legs to level the game with a 13-darter, a 114 finish and a 14-dart leg.
Checkouts of 148 and 129 then put the Austrian 2-0 up in the deciding set before he took out double 14 to claim victory on his World Grand Prix debut.
Suljovic will now face Australia's Simon Whitlock, who dropped only one leg in a straight sets victory over Andrew Gilding in the night's opening fixture, sealing the win with a 13-darter as he prevailed 3-0, 3-1.
"I expected a much tougher game than that and I think the key was starting with my first three darts in every leg, which makes a big difference," said Whitlock, the former European Champion.
"It wasn't too special a performance but it's a win. I've worked hard going into this and worked out which doubles work best for me and narrowed it down to two doubles which I've worked on, and it paid off for me.
"I've been playing really well lately and have had some good results and I'm comfortable again playing darts, so all the practice is paying off.
"I'm confident and that's a big thing, and no matter who I play I just want to play the best darts I can."
World Champion Gary Anderson began his challenge with a superb straight sets win over Scottish rival John Henderson, who was only able to win one leg as the number two seed averaged almost 98 in the double-start format.
Anderson took out 85 on the bull to claim the opening leg, and though Henderson levelled it was his opponent who landed seven perfect darts in the third leg before sealing the set 3-1 with a 96 finish.
Anderson then landed a 180 in the second set's opener and added a 174 score as he took the set without reply to seal a second round spot.
"I'm pleased with that and when the doubles go in like they did tonight it helps with your confidence," said Anderson. "My darts have been going well for the last week or so but there's a lot of great players still in the tournament."
Anderson will now meet Ian White, who enjoyed a 2-0 win over Jamie Caven as he moved into the last 16 in Dublin for a second time.
White took the opening set 3-1 before finding himself 2-1 down in the second, but after landing a 180 as he levelled he fired in another maximum before taking out 81 in the deciding leg to complete the win.
"At 2-1 in the second set I knew I had to hit back because if Jamie had taken that set he'd have been on a high, and the final leg went nicely for me," said White.
"My performances have been good this year and I had a nice win at the weekend on the ProTour, and I'm hitting a lot of 140s and 180s. I'm enjoying the game and it's going well at the moment.
"I want to start doing well on the TV stage because that's where everyone sees you, as opposed to the ProTour where you earn your bread and butter, so that's my goal now."
Robert Thornton - who landed a nine-dart finish in Dublin 12 months ago alongside Wade - impressed with a straight sets win over Daryl Gurney, averaging 97, hitting two ton-plus checkouts and six doubles from ten attempts.
Thornton finished 60 and 110 to move 2-0 up in the opening set, and though the Northern Irish ace hit back to level, a 106 checkout gave the former UK Open champion the set.
He shared the opening two legs of set two, but kicked off the third with a 160 score as he moved 2-1 up before finishing 56 on tops to move into the last 16.
"You're always nervous in the first round but I'm happy enough," said Thornton. "To average just under 97 is good but they don't matter if you don't hit your doubles and I did that too.
"I can look forward to playing Justin Pipe now that I've got this game out of the way because with the longer format you're not as edgy, and I'm feeling good."
Thornton now takes on Justin Pipe, who came from a set down to defeat Steve Beaton 2-1 in their first round clash.
Beaton had punished nine missed doubles from his opponent to win the opening set without reply, only for Pipe to turn the tables by taking the second set 3-1.
Pipe then finished 105 and 106 to move 2-0 up in the decider, and though Beaton hit back on tops, a 71 checkout sealed victory for the Taunton thrower.
"I was very nervous in the first set and I think Steve was as well, so to get through the first round is massive for me and I had to dig deep," said Pipe.
"My starting and finishing was okay, and I can relax and go up and play in the next round. I think it will be a different game."
Two-time World Grand Prix finalist Terry Jenkins - who turned 52 recently - overcame 2012 runner-up Mervyn King in another three-set thriller as he moved into the last 16.
King, using a new style of dart for the first time on TV, took the game's opening two legs before Jenkins replied with three in a row to move 3-2 up.
Jenkins also led 2-1 in the second before King battled back to win the set with a 13-darter to force a decider, but the Ledbury ace was to strong with a 12-darter, a 14-dart leg which featured a 100 checkout and a 76 finish as he sealed victory in style to continue his bid for a maiden major title.
"I'd love to win this event," admitted Jenkins. "I'm always good on the doubles and this is my favourite tournament, and over the longer format I'm more dangerous.
"When I was 2-0 down in the first set I still felt alright and pretty confident, and maybe Mervyn was trying too hard to win that first set with the darts. I punished him for it but he got it back in the second set.
"There were a lot of nerves there but I'm glad I managed to get the win.
The second round kicks off on Tuesday evening (7pm) with the four games from the top half of the draw, including reigning champion Michael van Gerwen's clash with Belgian ace Kim Huybrechts.
Number five seed Adrian Lewis takes on resurgent Mark Webster, Dave Chisnall faces Jelle Klaasen and Michael Smith meets Jamie Lewis.
Tickets for the partypoker.com World Grand Prix are available from the Citywest Hotel by email email@example.com or by calling 01 401 0505 (Outside Ireland 00353 1 401 0505).
partypoker.com World Grand Prix
Monday October 5
Andrew Gilding 0-2 Simon Whitlock
Justin Pipe 2-1 Steve Beaton
Mervyn King 1-2 Terry Jenkins
James Wade 1-2 Mensur Suljovic
Ian White 2-0 Jamie Caven
Phil Taylor 0-2 Vincent van der Voort
Gary Anderson 2-0 John Henderson
Robert Thornton 2-0 Daryl Gurney
Tuesday October 6 (7pm-11pm)
Michael Smith v Jamie Lewis
Dave Chisnall v Jelle Klaasen
Michael van Gerwen v Kim Huybrechts
Adrian Lewis v Mark Webster
Wednesday October 7 (7pm-11pm)
Robert Thornton v Justin Pipe
Mensur Suljovic v Simon Whitlock
Vincent van der Voort v Terry Jenkins
Gary Anderson v Ian White
Second Round - Best of five sets
* All Sets are the best of five legs. There will be no tie-break in any set.
* All legs must begin and end with a double, meaning that a player must hit a double before he can begin scoring in each leg.
Andrew Gilding v Simon Whitlock
0-1 - Whitlock finishes double four to claim the opening leg.
0-2 - Double two gives the Australian the second, after Gilding misses double 12 with three darts to steal the leg.
0-3 - Gilding lands a 180 but misses double five to punish further misses from Whitlock, who returns on double one to claim the set.~
1-0 - Double eight gives Gilding his first leg of the game.
1-1 - Whitlock levels by taking his second leg on double one.
1-2 - Both players land 180s in the leg before Whitlock finishes 54 on tops to move to the brink of victory.
1-3 - The Australian seals his second round spot in style with a 13-darter, hitting a 168 score to set up double eight.
Justin Pipe v Steve Beaton
0-1 - A scrappy opening leg goes to Beaton with his 12th dart at a winning double, after Pipe misses six chances to take the lead.
0-2 - Pipe lands a 180 but misses the bull and two further darts to take the leg, as double 16 moves Beaton two legs up.
0-3 - Beaton posts a third-dart double eight to seal the first set.
1-0 - Double 16 sees Pipe claim his first leg of the game.
1-1 - Beaton fires in a 180 before punishing two misses from Pipe by landing double eight to leve.
2-1 - Pipe again posts double 16.
3-1 - Tops gives Pipe the set as his revival continues.
1-0 - Beaton lands a 180, but Pipe takes out 105 on double 16 to move ahead.
2-0 - The Taunton ace produces a fine 106 finish as he moves to the brink of victory.
2-1 - Beaton opens the leg with a 146 score before hitting tops to keep his hopes alive.
3-1 - Pipe's comeback is complete as he takes out 71 on tops to seal the win.
Mervyn King v Terry Jenkins
1-0 - King - using a new design of darts in a major event for the first time - lands a 180 as he takes the opening leg, hitting double eight.
2-0 - Another double eight finish moves King two legs ahead.
2-1 - Jenkins finishes 72 on tops to get off the mark.
2-2 - The two-time finalist punishes misses from King at double 16 an eight by landing double eight to level the set.
2-3 - Tops sees Jenkins claim a third successive leg and the opening set.
0-1 - Both players land 180s before Jenkins takes out 68 to move ahead in set two.
1-1 - King finishes 76 on double eight to reply.
1-2 - Jenkins lands a 180 and tops for a 14-darter to move a leg away from the win.
2-2 - King keeps his hopes alive, landing a 180 and double 12.
3-2 - King saves the game to force a deciding set courtesy of a superb 13-darter.
0-1 - Jenkins lands a 180 and a 96 finish for a 12-darter to lead in the decider.
0-2 - Jenkins finishes 100 for a 14-dart leg to move to the brink of victory once more.
0-3 - The 52-year-old seals victory with a 76 checkout to claim the final set without reply.
James Wade v Mensur Suljovic
1-0 - Wade finishes 118 to take the opening leg.
1-1 - Suljovic takes out 93 on double 14 to level.
2-1 - Wade lands a 180 before finishing tops to punish the Austrian for a miss at double seven.
3-1 - Double ten gives the two-time champion the opening set.
1-0 - Wade posts a 180 in a superb 11-darter as he continues a fine start.
1-1 - Wade lands two maximums in the leg, only for Suljovic to take out double 16 for a 13-darter to level.
1-2 - A 114 checkout moves the Austrian ahead.
1-3 - Wade misses seven starting doubles, and Suljovic lands a 174 score and double 16 for a 14-darter to seal the set.
0-1 - Suljovic finishes 148 in superb style to move ahead in the match for the first time.
0-2 - The Austrian now finishes 129 on double 12 to move a leg away from the win.
0-3 - Double 14 seals a superb comeback victory from Suljovic, who avenges his quarter-final defeat to Wade in July's World Matchplay.
Ian White v Jamie Caven
1-0 - White lands a 180 and has enough cushion to initially miss three doubles to win the leg, with Caven missing two darts at double 16 to allow his rival back in on double two.
2-0 - Double three sees White move two legs up.
2-1 - Caven hits back with his first leg of the contest.
3-1 - Tops gives White the opening set.
1-0 - White fires in a 180 and double 16 to move a leg up.
1-1 - Caven finishes 53 on tops to level.
1-2 - Caven follows a 180 with a 76 finish to move ahead in the set.
2-2 - White lands a 180, and is again given a reprieve for missed doubles as Caven misses his chance to claim the set, as the Stoke thrower posts double one to move a leg away from the win.
3-2 - White fires in his fourth maximum of the game before finishing 81 on double 12 to seal the win.
Phil Taylor v Vincent van der Voort
0-1 - Taylor lands a 180 in the opening leg, but misses the bull for a 122 finish as van der Voort is handed a reprieve for earlier missed doubles by returning finish double two.
1-1 - TAYLOR MISSES THE BULL FOR A NINE-DART FINISH! Taylor opens with a 160 and adds a 180 to leave 161, hitting another treble 20 and the treble 17 before wiring the bullseye - but he returns to win the leg on double eight for a 14-darter.
1-2 - Taylor opens with a 160 score, but missed doubles allow van der Voort in on double ten.
2-2 - Taylor takes out 81 on double 12 to level.
2-3 - van der Voort kicks off with a 160 score before taking the set on double two.
1-0 - The pair trade 180s before Taylor lands double eight to move a leg up.
1-1 - van der Voort lands another maximum before levelling on double eight.
2-1 - Taylor kicks off with a 160, and though the Dutchman lands another 180 the 11-time champion lands double ten to take the leg.
2-2 - van der Voort fires in a fourth 180 of the set and double 16 to move a leg away from a huge win.
2-3 - Taylor misses double 16 to take out 105, and van der Voort seals a memorable win on double eight - becoming only the seventh player to defeat the Stoke legend in the World Grand Prix's history.
Gary Anderson v John Henderson
1-0 - Henderson lands the game's first 180, but Anderson finishes 85 on the bull to take the opener.
1-1 - Tops sees Henderson hit back to level.
2-1 - Anderson lands seven perfect darts by opening with a 160 and adding a 180 before hitting another treble 20, but he misses the treble 17 on the 161 combination to see his hopes of a nine-darter dashed, before he returns to take the leg in 12 darts.
3-1 - The World Champion kicks off another leg with a 160 score before finishing 96 for a 14-darter to seal the set.
1-0 - Another 14-dart leg sees Anderson lead in set two, courtesy of double 18.
2-0 - Double five moves the world number two a leg away from the win.
3-0 - Anderson fires in a 174 score before securing victory on double ten.
Robert Thornton v Daryl Gurney
1-0 - Gurney misses two darts at double 18, and Thornton capitalises by finishing 60 on tops to claim the first leg.
2-0 - The Scot also wins a high-quality second leg, opening with a 160 score before following a Gurney 180 with a 110 checkout of his own for a 12-darter to double his lead.
2-1 - Gurney finishes a 14-dart leg on double seven to get off the mark.
2-2 - The Northern Irish ace then finishes 62 on double 16 to square the set.
3-2 - Thornton claims the set in style, landing a 180 before completing a 12-darter with a 106 finish.
1-0 - Thornton misses three starting doubles but then scores 180 and 177 before finishing double 12 for a 13-dart finish.
1-1 - Gurney replies with a 180 - trading maximums with Thornton - before levelling by taking out 74 on double four.
2-1 - Thornton again kicks off with a 180 before landing double ten.
3-1 - Thornton seals victory with a 14-darter as tops completes a fine performance as he averages 97 and takes out six doubles from ten attempts.