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 play sent Nelson Semedo away and his brilliant cross, which bypassed four visiting defenders, was tapped in by Strand Larsen.
The recalled Jose Sa, replacing the injured Sam Johnstone in goal, 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.