City are third with 38 points from 19 matches, while the Reds lead the league with 52 points and have a game in hand, reports Efe news.
Wolves, meanwhile, have climbed to 5th place with 30 points while becoming only the second team in any league to prevail in a season series against a squad coached by Pep Guardiola, having beaten City on October 6 in Manchester.
The first key moment in what would turn out to be a drama-filled Friday night at Wolverhampton's Molineux Stadium came barely 10 minutes into the contest.
Wolves' Conor Coady got a ball to Diogo Joto behind the City defence, prompting a desperate Ederson to rush to the edge of the area in bid to deny the striker.
Missing the ball, the City keeper brought down Joto and was sent off with a red card for denying a goal-scoring opportunity.
But even with the man advantage, the hosts struggled to generate offence and City drew first blood.
Leander Dendoncker fouled City's Riyad Mahrez in the area and while the referee initially declined to award a penalty, he reversed himself based on VAR.
Raheem Sterling took the kick, but Wolves keeper Rui Patricio made the stop and Coady cleared the ball.
Yet VAR intervened again, citing Coady for encroachment and ordering a second kick. Patricio turned aside Sterling's second shot, but the City striker was able to gather the rebound and put it in the net to make it 1-0 for the visitors.
Sterling, assisted by Rodri and Kevin de Bruyne, scored again just five minutes into the second half and the two-time defending champions looked set to claim all three points.
It was then that Wolves' Adama Traore, author of both goals in October's 2-0 victory at the Etihad, started to make his presence felt, needing just five minutes to pull back a goal for the hosts.
City preserved the lead until the 82nd minute, when Wolverhampton's top scorer, Raul Jimenez, converted a Traore cross for the equalizer, his 17th goal of the season in all competitions.
Matt Doherty completed the comeback, delivering the winning goal for Wolves in the final minute of regulation time.
( With inputs from IANS )