Number five seed Wright had never previously won past the last 16 in the Grand Slam before this event, but continued his series of assured displays by landing four ton-plus checkouts and ten 180s to see off the sport's greatest ever player.
Wright raced into a 5-0 lead in a clinical opening to the contest before six-time Wolverhampton Civic champion Taylor found his range to claim four of the next five as he cut the gap to 6-4.
Wright then missed double 12 for a nine-dart finish as he edged 7-4 up, and after Taylor cut the gap to one leg the Scot took out brilliant checkouts of 152 and 101 in successive legs to pull away once more.
Taylor followed a 14-darter with a thrilling 143 finish to again hit back to within a leg at 9-8, but Wright once more edged away with two killer checkouts, as he took out 141 and 121 in taking a 13-8 lead.
Finishes of 62 and 64 kept Taylor in touch at 14-10, but Wright landed a tenth 180 of the contest in closing out a memorable win with double eight for a 14-dart leg.
"I felt really calm and I enjoyed the game - I was so relaxed and I thought I played a nice game of darts," said Wright, who will also move above Taylor and Adrian Lewis to third in the PDC Order of Merit following this event.
"It was like I was playing Phil back at my house, just with a little bit of noise in the background! It was a great game and it was nice to be involved in it.
"I felt in control and then Phil took over, but in the past I've relaxed and let Phil play his game. Phil has come back and beaten me before and I was waiting for it again, but I've learned a lot and I focused more.
"Finishing is the most important part of the game and the hard work in practice paid off tonight. I'm really happy."
Earlier, reigning champion van Gerwen romped into the last four with a 16-3 demolition of Brendan Dolan, who had won through to his first Wolves Civic quarter-final but was unable to match the world number one's scoring power.
Van Gerwen took the opening five legs without reply to take command, finishing 104 and 121 in the process, before Dolan stepped in to claim leg six.
The Dutch star, though, finished 90 for another break of throw as he pulled away with eight successive legs to move 13-1 up, with Dolan landing tops to hit back with two legs.
However, the Northern Irish ace missed his chance to continue the fightback as van Gerwen stepped in to win the next three legs and secure his semi-final place.
"Of course, 16-3 is a good win but to be fair Brendan didn't really put me under pressure in this game," conceded van Gerwen. "I'm glad I got through but I didn't play fantastic darts, I was a bit sloppy on my doubles but I won the game.
"I'd rather have a bit more action, but it's nice to win like that. Brendan said sorry that he didn't give me a game, maybe I was too relaxed but if it was closer he wouldn't be in that position.
"I feel good, I feel confident and I can prepare for the semi-finals now."
Wright has not defeated van Gerwen since the 2015 Japan Darts Masters, with the Dutchman's 15 successive wins including triumphs in the finals of this year's UK Open, World Series of Darts Finals and in three European Tour events.
However, Wright added: "It will make a change not playing him in the final and I'm looking forward to it. I believe I've got the next step and we'll have to wait and see."
The quarter-finals conclude on Saturday (8pm) with the remaining two matches, with 2010 Grand Slam runner-up James Wade taking on emerging star Chris Dobey before World Champion Gary Anderson comes up against 2012 Wolverhampton winner Raymond van Barneveld.
Van Gerwen is now the 4/9 favourite to take the title on Sunday with Sun Bets, the official betting partner of the SINGHA Beer Grand Slam of Darts.
Anderson is the 4/1 second favourite, with Wright 6/1, Wade 12/1, van Barneveld a 16/1 chance and Dobey the 100/1 outsider.
SINGHA Beer Grand Slam of Darts
Friday November 18
Michael van Gerwen 16-3 Brendan Dolan
Peter Wright 16-10 Phil Taylor
Saturday November 19 (8pm)
Chris Dobey v James Wade
Gary Anderson v Raymond van Barneveld
Best of 31 legs