The Premier League champions' perfect start to the season came to an abrupt end at Molineux on Saturday.
Match Report
Pep Guardiola's side enjoyed the better chances in the early stages with Manuel Akanji having an effort from long range wide of the goal.
Wolves remained in the game throughout however, and after a dazzling run from Pedro Neto the hosts took the lead against the run of play on 13 minutes after a deflection from Ruben Dias.
City were not at their best through much of the first-half but they managed to equalise following the interval with Julian Alvarez scoring a stunning free-kick from the edge of the box.
Despite surrendering their lead, Wolves remained dangerous on the counter and just minutes later restored their advantage with a goal from Hwang Hee-chan.
Match Events
0' The match is about to start!
13' OWN GOAL! Wolves 1-0 Man City (Ruben Dias)
30' Foden's shot stopped
39' Yellow Card! Lemina booked
51' Haaland's shot stopped
58' GOAL! Wolves 1-1 Man City (Julián Álvarez)
66' GOAL! Wolves 2-1 Man City (Hwang Hee-Chan)
Line-ups
Wolves XI: Dawson, Lemina, Semedo, Jose Sa, Hwang Hee-Chan, Kilman, Pedro Neto, Matheus Cunha, Rayan Aït-Nouri, Toti Gomes, João Gomes
Subs: Sarabia, Doherty, Daniel Bentley, Castro, Sasa Kalajdzic, Santiago Bueno, Joe Hodge, Fábio Silva, Boubacar Traoré
Man City XI: Walker, Kovacic, Ake, Ederson, Ruben Dias, Akanji, Haaland, Foden, Julián Álvarez, Matheus Nunes, Jérémy Doku
Subs: Carson, Stefan Ortega, Grealish, Kalvin Phillips, Sergio Gómez, Josko Gvardiol, Oscar Bobb, Rico Lewis