Pep Guardiola was on the pitch, perplexed at John Stones’s winner halfway through the final minute of stoppage time being disallowed for offside against Bernardo Silva. Wolves’ coaching staff and ­substitutes celebrated like they had clinched a first victory of the season. Then the message rained down that the VAR, Stuart Attwell, had recommended the referee, Chris Kavanagh, go to the monitor to take another look.

Moments later the seesaw of emotions flipped again, Wolves apoplectic. Suddenly, Gary O’Neil, of all people, found himself playing peacemaker, trying to prevent his assistants and substitutes from confronting the officials.

Related: Wolves 1-2 Manchester City: Premier League – live reaction

Pablo Sarabia was booked for his protestations; João Gomes, sat on the drinks cooler after being withdrawn minutes earlier, bereft. For Guardiola and Manchester City’s players, in their jasper red third strip and now a club-record 31 games unbeaten in the league, ecstasy. Stones blew kisses towards the delirious away end, jumped over the advertising hoardings, and Josko Gvardiol, who scored a beautiful equaliser in the first half, grabbed Stones so tightly he appeared to rip his shirt. The champions had found a way.

“We are not used to winning games at the end, like Jürgen Klopp at Liver­pool – it happened many times,” the City manager said. “It is a good flavour for us.”

Sweet for City but sickening for Wolves; another agony-inducing VAR moment. Six months ago Wolves, who voted against the use of VAR technology in the close season, were incensed after Max Kilman saw a 99th-minute equaliser disallowed because Tawanda Chirewa was deemed to be blocking the view of Lukasz Fabianski. This time the referee visited the VAR monitor, with a disbelieving Matheus Cunha over his shoulder, and returned a verdict in Guardiola’s favour. As a deflated O’Neil said afterwards, the PGMOL’s key incidents panel will argue its case but it will not wash with Wolves.

With about 30 seconds of five minutes of added time to run, City won their 18th corner of the match. Phil Foden, on as a substitute, curled an inswinger towards the front post, where Stones powered in past José Sá. O’Neil’s assistant, Shaun Derry, sank to the turf in the home technical area.

Wolves sacked their set-piece coach, Jack Wilson, formerly of City, after their humiliating 5-3 defeat at Brentford but they again came unstuck from a corner. But as the ball came into the box Silva backed into Sá, who replaced the injured Sam Johnstone, and two seconds later the ball was in the back of the Wolves net. Santiago Bueno booted it clear in anger. O’Neil was frustrated with the refereeing inconsistency but also disappointed at his side’s defending.

Until then, they had been everything O’Neil asked after that alarming defeat in west London. Of course, a hulking 6ft 4in ­Norwegian, a 24‑year‑old No 9 would open the scoring. Only it was not Erling ­Haaland but Jørgen Strand Larsen who capped a slick Wolves move to give City something to think about.

Guardiola’s side equalised courtesy of Gvardiol’s graceful strike but just as it seemed Wolves would be rewarded for digging deep into the energy reserves to eke out an ­invaluable point, they were winded by Stones’s pure header. By this point next weekend, Wolves will have faced seven of the top eight.

Wolves’ appetite to keep a first league clean sheet since February had appeared both physically and mentally exhausting. At one point Toti Gomes did an impromptu ­headstand on the goalline after desperately hacking away a smacked shot by Silva. Craig ­Dawson and Mario Lemina were alert to every ball. O’Neil frantically tapped his ­temples as André shepherded the ball out of play for a Wolves goal‑kick 29 minutes in, a rare luxury after ­absorbing relentless pressure as City sought an equaliser.

Four ­minutes later it arrived, Jérémy Doku, wide on the left, ­shifting the ball to Gvardiol 20 yards from goal. City attacked in ­numbers, every outfield player perched on the perimeter of the Wolves box. ­Gvardiol’s first touch allowed the ball to roll across his body and with his next he curled a right-foot shot into the top corner, via Sá’s fingertips.

Sá had a fine game. He made a smart early save down to his right to deny Silva and another in first-half stoppage time to push Savinho’s punched effort out for a corner. In the second half he plunged to his left to force Rúben Dias’s effort round his left post and Wolves survived a couple more scares but City did not pene­trate the hosts quite so easily. ­Gonçalo Guedes appeared minded to run the clock down with 83 ­minutes gone.

Foden arrived midway through the second half as Guardiola attempted to dial up the pressure. Then he later turned to Matheus Nunes, the former Wolves midfielder whose arrival was jeered by the home support. Plenty more anger ensued.