The Citizens fell behind in Sunday's away clash after Jorgen Strand Larsen broke the deadlock in the seventh minute.
Josko Gvardiol provided the Man City response, equalising in the 33rd minute to send the two teams into the break on level terms.
Pep Guardiola's side looked set to be heading towards a draw until John Stones headed home from a corner in the fifth minute of stoppage time.
Referee John Brooks was sent to the monitor to decide whether the offside Bernardo Silva had impeded Jose Sa for Stones's late winner.
The referee ultimately decided to award the goal, ensuring Man City could celebrate a third consecutive victory in all competitions.
Man City set new unbeaten record with Wolves win
Not only were Man City able to celebrate a victory, but they also celebrated the fact they set a new club record with their narrow win.
The Citizens have set a new club record for the longest unbeaten league run in their history, having avoided defeat in their last 31 top-flight matches.
Man City have won 25 and drawn six Premier League games since they suffered their most recent defeat against Aston Villa in December 2023.
The Premier League winners have ultimately surpassed the 30-game unbeaten league run they put together from April 2017 to January 2018.
Man City's profilic defender
Like his teammates, Gvardiol also had plenty to celebrate after he scored his first Premier League goal of the season.
Impressively, the Croatia international has now scored six Premier League goals in the current calendar year, making him the highest-scoring defender in the English top flight in 2024.
Man City's successful away outing briefly moved them into top spot, before they dropped down to second following Liverpool's win over Chelsea.
The Citizens will look to extend their club-record run to 32 league games when they play host to Southampton next weekend.
Before that, Man City will welcome Sparta Prague to the Etihad Stadium for Wednesday's Champions League fixture.