City's home campaign began with a deafening wave of noise from 47,287 spectators following their exploits in a stiflingly hot Nou Camp against Barcelona in midweek.
Early season momentum from their trips to Blackburn and Barcelona continued into their first home game of the season after they reaped a richly deserved goal following a patient build-up in the first half.
Wayne Bridge's cross was deflected away from Gareth Barry, who was shaping to volley, but fell kindly to Carlos Tevez on the other side of the area who duly found his strike partner Adebayor in space.
The Togolese striker made no mistake in slotting the ball into the space between Wayne Hennessey and his near post - cue rapturous applause.
Their first-half performance deserved more goals, but efforts by City found Hennessey in good form, producing saves from Bridge, Adebayor, and Tevez in the first half.
It seemed that City might pay for their profligacy in front of goal despite their attractive approach play and, for sure, it was the visitors who found a second wind after the break.
After weathering the first-half storm Wolves manager Mick McCarthy made two changes at half-time, bringing on George Elokobi to shore up the defence and Kevin Doyle to join Andrew Keogh upfront and the new front pair helped Wolves step up a gear against a rapidly tiring City side.
Both Keogh and Doyle had chances presented to them early in the second half and although Keogh struck the bar with just over 20 minutes to go, the rapidly tiring City defence held together just enough to repel Wolves.
City might have had a second goal shortly after Keogh had rattled the woodwork had Robinho's tap-in from Wright-Phillips' cross not been adjudged offside, but the Citizens will feel lucky to have earned the three points.