But three second-half goals - including two in the final eight minutes - saw Wolves complete a league double over City on a desperately disappointing night in the Midlands.
After a cagey opening period, the game exploded into life when Ederson was shown a red card for bringing down Diogo Jota on the edge of the area.
Connor Coady’s sublime ball over the top put Jota clear, he knocked it past the onrushing Ederson who clipped the Wolves man and left the referee with little choice but to brandish a straight red.
It was a disastrous moment that made an already difficult assignment look even harder.
But this City side is packed with character, and 13 minutes later we ahead after a period of chaos and confusion.
Riyad Mahrez went on a mazy run inside the area and was taken down by Leander Dendoncker. Martin Atkinson initially waved City’s claims for a penalty away, but a lengthy VAR check overturned the decision and a spot kick was justifiably given.
Raheem Sterling stepped up to take it – but his penalty was saved by Rui Patricio.
However, it was ordered to be retaken after encroachment by Wolves players and Sterling stepped up again – despite Pep Guardiola seemingly gesturing from the bench to change the taker – and again Patricio made the save. This time, though, Sterling tapped home from the rebound to put City ahead.
Wolves has the first big chance of the second half. Raul Jimenez’s brilliant scooped pass put Jota through but his effort from close range went over the bar. He should have done better.
And City took full advantage of the home side’s profligacy when Sterling doubled our lead. Kevin De Bruyne’s instinctive pass put the forward through on goal and he produced a quite brilliant chip to beat Patricio and send the away end into a frenzy of emotion.
Traore halved the deficit when his low strike went in on off the post, before Wolves equalised with eight minutes left on the clock when Jimenez poked home from Traore's cross after Benjamin Mendy had his pocket picked on the byline.
And Wolves found a winner with a minute remaining when Matt Doherty curled one into the bottom corner from the edge of the area.
Sterling hit the bar with a free-kick from 20 yards, denying him a hat-trick and City what would have been a memorable equaliser, and Wolves saw the game out to deliver what could well be a fatal blow to our already slender title hopes.
Sterling now has 59 Premier League goals for City, moving him ahead of Carlos Tevez on the list of City’s goalscorers.
Only Sergio Aguero and Yaya Toure have scored more for City.
What it means
The result sees City remain third, one point behind Leicester, who lost at home to Liverpool on Boxing Day.
The Merseysiders have a healthy lead at the top. They have dropped just two points all season and are currently 13 points ahead of Leicester with a game in hand.
City host Sheffield United on Sunday at 6pm, meaning Guardiola and his backroom team have less than 48 hours to prepare for our next assignment.
It’s a difficult task and Guardiola is likely to make significant changes when the Blades visit the Etihad given his players have so little time to rest and recover from tonight’s exertions.