Waltham Abbey's West had only qualified for the World Grand Prix by reaching the final of the last Players Championship before the cut-off just over a week ago - but showed that he belongs amongst the world's best with an inspired display.
Taylor, the 11-time World Grand Prix winner, hit back from a leg down to take the opening set 3-1, and shared the first four legs of the second set to move a leg away from the win.
West, though, finished 101 for a second time as he took the set to level before winning the decider 3-1 for the biggest win of his career.
"I'm gobsmacked," said West, the world number 52 who now meets Daryl Gurney in Wednesday's second round. "It's the biggest moment in my whole darting life - there's no words for it.
"I'm glad I battled through it and got through. Phil's an absolute legend and no-one can express what he's done for this game - it's an honour to play him even, and to beat him is unreal.
"I believe in myself, I know what I can do and I've just got to carry it on. If I can, I'm going to go far."
Northern Ireland's Gurney, who returned to action on Friday after a month sidelined with a broken bone in his throwing hand, overcame Austria's Mensur Suljovic in a deciding leg as he moved into the last 16 for the first time.
"I'm over the moon and so glad to get through that," said Gurney. "I've not won here before so I'm very pleased because Mensur's a great player.
"My hand's still not 100 percent but maybe I need to break it more often if it helps me get through!"
World number one van Gerwen moved through to a meeting with debutant James Wilson in round two by coming from a set down against Steve Beaton.
Beaton produced an outstanding 135 finish as he claimed the opening set 3-1 from a leg down, but van Gerwen reeled off six straight legs to storm through, sealing the win with a 118 checkout.
"I'm really happy with my performance," said van Gerwen, who averaged an impressive 97 in the double-start format. "Steve did well but I think I produced something really special in the last six legs.
"The format goes up now and it suits me because you don't have to worry about one mistake."
Huddersfield's Wilson also came from a set down, against Ireland's Mick McGowan, as he sealed victory by claiming the decider 3-0 on his debut in the double-start format.
"I took a bit of time to settle in and I was a little bit nervous, but I got into my game," said Wilson, ranked 48th on the PDC Order of Merit. "I want to keep playing the way I am and hopefully things will keep going my way because I'm doing quite well at the minute."
World number five Peter Wright joined Taylor in being knocked out as he lost in straight sets to 2011 World Grand Prix runner-up Brendan Dolan, who now meets 2013 finalist Dave Chisnall.
"It's a very special win because my form hasn't been great this year," said Dolan, who had warmed up for the event with his marriage to Teresa last week. "I got stronger as the game went on and it's a great boost.
"Dave's another Premier League player and he's a brilliant player. He's got to the final of this tournament before so it should be nip and tuck."
Chisnall, meanwhile, overcame a power cut - forcing a 20-minute delay - and the loss of the first set against Robbie Green before he moved into the last 16.
"I didn't turn up for the first set, and the power cut probably helped me," admitted Chisnall. "I wasn't at my best but I got through it and I can look forward now to the next round."
Alan Norris celebrated his World Grand Prix debut with a 2-1 defeat of number eight seed Michael Smith, who took the first set 3-1 but saw his rival take out 156 and 136 on his way to victory as he set up a meeting with Australia’s Simon Whitlock.
Whitlock was another player to win from a set down as he overcame Joe Cullen, winning six of the game's final seven legs to continue his revival, after winning his first ranking title for two years on Saturday.
The second round of the £400,000 double-start tournament begins on Tuesday, with the four matches including World Champion Gary Anderson up against Australia's emerging Kyle Anderson.
World number three Adrian Lewis meets two-time Dublin finalist Raymond van Barneveld, two-time runner-up Terry Jenkins faces young Dutch star Benito van de Pas and Stephen Bunting takes on Kim Huybrechts.
Unibet World Grand Prix
Monday October 3
First Round x8
Dave Chisnall 2-1 Robbie Green
Mick McGowan 1-2 James Wilson
Mensur Suljovic 1-2 Daryl Gurney
Michael Smith (8) 1-2 Alan Norris
Joe Cullen 1-2 Simon Whitlock
Phil Taylor (4) 1-2 Steve West
Michael van Gerwen (1) 2-1 Steve Beaton
Peter Wright (5) 0-2 Brendan Dolan
Tuesday October 4 (7pm)
Second Round x4
Terry Jenkins v Benito van de Pas
Stephen Bunting v Kim Huybrechts
Gary Anderson v Kyle Anderson
Adrian Lewis v Raymond van Barneveld
Wednesday October 5 (7pm)
Second Round x4
Alan Norris v Simon Whitlock
Brendan Dolan v Dave Chisnall
Steve West v Daryl Gurney
Michael van Gerwen v James Wilson
Second Round - best of five sets, best of five legs per set.