John Stones' dramatic stoppage-time winner kept Manchester City in touch with Premier League leaders Liverpool as the champions beat battling Wolves.
The defender's header - in the fifth minute of injury time - was given when referee Chris Kavanagh awarded the goal on review, to the hosts' fury, after it was initially ruled out for offside.
Josko Gvardiol had earlier cancelled out Jorgen Strand Larsen's opener for Wolves, who remain winless this season and are bottom of the Premier League.
City made the early running at Molineux but were stunned on seven minutes when neat build-up sent Nelson Semedo away and his brilliant cross, which bypassed four City defenders, was tapped in by Strand Larsen.
The recalled Jose Sa, in for injured goalkeeper Sam Johnstone, denied Bernardo Silva soon after as City controlled the game but they had to wait until the 33rd minute to level when Gvardiol found the top corner from 20 yards.
Yet it did not give them an immediate platform for victory and the visitors were met by an undaunted opponent who denied them space, although only an excellent low save from Sa denied Savinho in first-half stoppage time.
Another Sa stop kept Ruben Dias out as City camped in the hosts' half but they were almost caught out by a rare Wolves break, Matheus Cunha shooting wide.
Pep Guardiola summoned Phil Foden and Jack Grealish from the bench but City were made to wait until deep into stoppage time to find a winner.
Stones headed in Foden’s corner, only for Silva to be ruled offside as he was standing in front of Sa, but, with the City players watching on, referee Kavanagh gave the goal to break Wolves’ hearts.
An early marker in the title race?
Given the relentless efforts of Liverpool and Arsenal's continued presence this season every point dropped will be crucial and City were on the brink of losing ground. Instead, they temporarily went top before Liverpool beat Chelsea later on Sunday.
Of course, City lost 2-1 at Molineux last season and still went on to win a fourth straight title but with Arne Slot’s near perfect start at Anfield and Arsenal continuing to improve under Mikel Arteta, Guardiola will know his side can ill afford to fall behind.
When they eventually found a way through, it was not through an intricate passing move but a last-gasp corner and moments like that will only strengthen their resolve to win a fifth straight crown.
Wolves deserve huge credit for their rearguard action and City looked like they lacked the ideas and ingenuity to find a winner until finally coming up with an answer.