It was City who started the stronger and they might have led within a minute when Carlos Tevez struck from distance, but it just drifted high of the bar.
Wolves also worried the City defence in the early stages, however, after good work from David Davis barely three minutes into the match.
Sergio Aguero so nearly added City's first after seven minutes, but his low shot just drifted past the post.
Wolves began to enjoy a spell of possession as the half developed, however, with Michael Kightly looking dangerous on the wing.
Davis struck a powerful effort for the home side from the edge of the box after 12 minutes, but City goalkeeper Joe Hart clawed the ball to safety.
City were next to come close via Samir Nasri after 16 minutes, but he dragged his effort just wide after good work from Aguero, before the latter shot wide after 20 minutes.
City did eventually take the lead, however, after 27 minutes when Aguero converted from close range after a fine pass from Gael Clichy.
Chances remained few and far between in the latter stages of the half, with City leading courtesy of Aguero's strike after 27 minutes.