If this is where Manchester City practically lost their title, at least they can say they did not relinquish it without a fight. But, not for the first time this season, they lacked sangfroid in the heat of this extraordinary battle and that cost them dearly. It is, in fairness, very hard to stay cool when being attacked by this excellent Wolves team – and when trying to chase down Liverpool, who are now 14 points clear of City with a match in hand.

Given the size of that lead, Pep Guardiola says his team’s most realistic ambition is to reclaim second place from Leicester. He said if they relent in their pursuit, they risk missing out on the top four. “We cannot prioritise cup competitions because if so, next season we will not be in Europe,” he said. “We have to think about Leicester. We have a chance to recover second position.”

For a while it looked like City would triumph here with the aid of VAR and over remarkable adversity, including self-inflicted wounds. Ederson was sent off in the 12th minute for clattering into Diogo Jota outside his area, then Raheem Sterling had the same contentiously awarded penalty saved twice by Rui Patrício. Yet still 10-man City established a two-goal lead. First Sterling rolled in the rebound from his retaken penalty, then he scored in the second half to move tantalisingly close to victory.

But not close enough. Wolves, again inspired by the phenomenal Adama Traoré, came storming back with three exquisite goals in the last 35 minutes. Traoré scored the first of them before creating an equaliser for Raúl Jiménez, who later played a beautiful pass to tee up Matt Doherty for a winning goal that ignited wild celebrations at Molineux. And, no doubt, on Merseyside.

Guardiola’s plans ran into a complication even before kick-off here, as illness afflicted Gabriel Jesus and forced City to draft in Sergio Agüero. An aristocrat’s problem if ever there was one, but City had wanted to ease their record goalscorer back into action after a thigh injury and would have preferred not to make this the match in which he made his first start for over two months.

As it turned out, Agüero was invited to rest up again after only 12 minutes, as Guardiola had to sacrifice him to introduce a replacement goalkeeper following the dismissal of Ederson. The referee, Martin Atkinson, ordered the keeper off after he charged out of his box and brought down Jota, who beat him to a pass over the top by Conor Coady. In came Claudio Bravo for his first Premier League appearance since November’s defeat at Liverpool. João Moutinho’s free-kick made for a comfortable reintroduction. Neither manager grumbled about the red card, nor would they offer their views on what happened in the 22nd minute – but the home crowd were not coy about expressing their anger at the decision to award City a penalty when Riyad Mahrez fell spectacularly in the box following contact with Leander Dendoncker. The infringement was not apparent to most people in the stadium but this is the age of mass surveillance: VAR spotted Dendoncker treading on the Algerian’s foot.

Patrício saved Sterling’s penalty but then, again on the recommendation of VAR, the referee ordered it to be retaken due to encroachment. Patrício made another save but was helpless to stop the relieved Sterling from stroking in the rebound. A few bozos in the stands vented their anger by flinging objects on to the pitch. The Football Association has opened an investigation.

City did well to protect their lead until half-time. Guardiola replaced Mahrez during the break with 18-year-old Eric Garcia as City buttressed their defence. Wolves soon showed the tempo that the youngster would have to get used to, as Jiménez and Jota cut through City’s backline with wicked finesse. Jota flicked the ball over the bar after running on to the Mexican’s lovely looped pass.

Soon Sterling produced an even finer chip. After being released by Kevin De Bruyne, Sterling ran into the box and did what he had been unable to do from the penalty spot, beating Patrício with a deadly dink.

That gave City an extra cushion but they could not sit comfortably for long. Five minutes later Sterling lost possession in midfield to Rúben Neves, who helped the ball on to Traoré, whose devastating directness City have learned to dread. After scoring twice at the Etihad, he slashed City’s lead here by ramming a long-range shot into the bottom corner.

Wolves attacked in waves after that. Traoré almost found a way through them again but was foiled by Bravo. City enjoyed a let-off as Romain Saïss nodded wide from six yards. Then Rodri made a critical intervention at the back post to deny Doherty.

As City clung on, Benjamin Mendy tried to shepherd the ball out of play near the byline, a decision that Traoré soon made him regret. The Spaniard shunted the defender aside before crossing for Jiménez to slide the ball into the net from close range. Doherty then struck a superb winning goal, running in from the right and exchanging slick passes with Jiménez before firing into the net.

In the dying seconds Sterling struck a free-kick against the crossbar. There was to be no happy ending for City. “We have to adjust mentally to the situation and prepare the next games,” said Guardiola.