Wolves stunning comeback secured a 3-2 win over Pep Guardiola's side in a frantic second-half at Molineux.
The Wanderers now move to fifth place in the Premier League table on 30 points, one above Tottenham Hotspur and two behind Frank Lampard's Chelsea.
Story of the game
Emerson's early sent off in the 12th minute as Diogo Jota was bought down on the edge of the area by the Brazilian keeper, this left referee Martin Atkinson with little choice.
Not long after the visitors were rewarded a penalty after Leander Dendoncker made contact with Riyad Mahrez in the 18-yard box causing the Algerian to lose balance. Penalty claims from the players and the stands were heard but Atkinson initially waved the claims away. Until VAR got involved.
More VAR controversy
After some minutes of tension and wait, VAR overturned the initial decision and City were rewarded a penalty in the 25th minute. Sterling saw his conversion saved by Rui Patricio. However, VAR communicated that there was an encroachment, Sterling stepped up to retake from the spot and although Patricio saved again, the rebound was converted by the 25-year-old.
Nuno Espirito Santo's men fell short to two goals just after the break, Kevin De Bruyne's through ball fell in the path of the forward who chipped the ball past Patricio.
The home side's chance to get back into the game came in the second half when Raul Jimenez's pass put Jota through,whose effort from close-range was just over the bar.
It was almost an instant reaction from the home side as Adama Traore halved the deficit from a Ruben Neves' pass. The Spaniard's low strike initially touched the post and was then found at the back of the net before equalising with eight minutes left on the clock.
City's Benjamin Mendy got distracted at his end's byline allowing Traore to pocket pick and provide a low cross to the box to which Jimenez poked home from close-range.
The winner was found when Matt Dougherty curled Jimenez' back flick pass from the edge of the box.
Denied by the woodwork
In the latter stages of the game, the Citizens were rewarded a 20-yard free-kick but Sterling's shot hit the bar denying him a hat-trick. Had it gone in, it would have been a massive blow for Nuno's men after their efforts were paid off.
Takeaways from the game
The title race is practically over
While City could not afford to slip up to maintain their title race to rivals Liverpool, this wasn't the case and the Reds are sitting comfortably in first place, 13 points clear. They also have a game in hand and the advantage could extend to 16 points.
After tonight's defeat, the Premier League title may as well be handed to the Merseyside club.
Adam Traore in fine form
The 23-year-old has reached the highest of his career after a brilliant start to the season. His goal to get Wolves back into the game meant he has now scored four this season so far and three more than last term.
He also picked up his seventh assist in all competitions after a well-executed pass to Jimenez to score the equaliser.
Should the penalty have been retaken?
The first penalty converted by Sterling saw Patricio save it but moments later, the referee was informed by VAR to retake the penalty. The reason behind this was due to Conor Coady was adjudged to have encroached before cleaning the ball.