City looked like failing to capitalise on Arsenal's slip-up at Bournemouth as they were being held on Sunday after Jorgen Strand Larsen's early opener for the dogged hosts had been cancelled out by Josko Gvardiol.
But Stones climbed highest in the fourth minute of added time to power home Phil Foden's corner and spark wild scenes of celebration.
But they were cut short after Bernardo Silva was eventually flagged for offside as he stood in front of goalkeeper Jose Sa.
But after referee Chris Kavanagh was asked to check the pitchside monitor, he ruled that a backtracking Silva was not interfering with play and the goal stood.
It was a get-out-of jail-free card for City, who were well below their best, but still moved three points clear of the Gunners.
It also extended City's unbeaten streak to a club-record 31 league games, beating a mark Pep Guardiola's team had set in 2018.
For Wolves, it was heartbreak and not what they deserved after a good performance, but they have now claimed just one point from the opening eight games.
Gary O'Neil's team could not have dreamed for a better start at Molineux as they went ahead in the seventh minute.
After beating the City press, Nelson Semedo was set free down the right and his excellent cross bisected Ederson and the City defence, allowing Strand Larsen to slide into an empty net at the far post.
Seconds after the restart, City almost equalised as Silva set a low curling effort that was destined for the far post until Sa got across to keep it out with a fine save.
City were pushing for an equaliser, but that left them exposed and another lightning quick break should have seen Wolves double their lead in the 19th minute.
Joao Gomes sent Semedo through on goal, but the Portuguese's touch was heavy at the vital moment, allowing Ederson to come out and block his shot.
City equalised in the 33rd minute, when Gvardiol received the ball on the corner of the penalty area and sent a superb 20-yard dipping shot into the top corner.
They almost went into halftime in front but Sa produced another outstanding low save to keep out Savinho's effort.
The recalled goalkeeper, in for the injured Sam Johnstone, was again called into action early in the second half to keep out a Ruben Dias shot from distance.
But for all their possession, Pep Guardiola's side were struggling to break down a well organised and compact Wolves defence, with the introduction of Foden and Jack Grealish making little difference.
The match seemed destined to finish a draw until the corner in the fifth minute of added time which Stones headed home.
17°C