Raheem Sterling scored his 100th Premier League goal as Manchester City eventually forced their way past dogged Wolves who had Raul Jimenez controversially sent off in first-half injury time.
Jimenez received his yellow and red cards within 31 seconds of each other after tripping Rodri and then failing to retreat from the resulting free-kick.
With an extra man, City finally took advantage when Joao Moutinho was penalised for handling Bernardo’s cross – against disputed by Wolves – and Sterling rolled in the 66th minute penalty.
City hit the top of the Premier League for the first time last weekend and the strength of options available to Pep Guardiola was underlined by having Kevin De Bruyne, Phil Foden and Kyle Walker on the bench.