After a hard-fought FA Cup tie, the Citizens avoided an unwanted replay thanks to a rare goal from the marauding right back
Despite The Citizens enjoying the best of the action for the majority of the game, they looked unable to break Stoke down for the most part, with David Silva coming closest in the first half with a curling effort that rattled the woodwork.
However, an unlikely hero emerged in right back Pablo Zabaleta as the Argentinian marauded forward with five minutes remaining, diverting the ball home adeptly and putting the Premier League champions through to the next round of the FA Cup.
Tony Pulis decided to wring the changes from the side that lost 3-1 against Swansea, with Ryan Shotton, Andy Wilkinson, Michael Kightly and Kenwyne Jones all replacing Dean Whitehead, Geoff Cameron, Charlie Adam and Peter Crouch.
Roberto Mancini, meanwhile, chose to tinker solely with his backline as he rested Joe Hart, Gael Clichy and Masteo Nastasic, with Costel Pantilimon, Joleon Lescott and Alexander Kolarov slotting into the team in their absence.
After early half-chances were spurned by Carlos Tevez and Robert Huth on either side, it was almost twenty minutes before the first clear-cut chance fell Manchester City's way; with a quick free-kick from James Milner catching Stoke unaware, David Silva took one touch before curling it goalwards, beating Sorensen but being denied by the post.
Despite the away side's growing pressure, the Potters were next to truly threaten the goal as, after a deep free-kick was turned goalward by Robert Huth, Ryan Shawcross was there to turn it home, but, unfortunately for the home side, he was in an offside position and the opener was duly ruled out.
With the Citizens continually proving unable to break the home side down in the remainder of the first half, their problems were exacerbated as captain Vincent Kompany hobbled off injured with a suspected calf strain.
The second half got off to a contentious start as Glenn Whelan dived in dangerously on Javi Garcia but, with Howard Webb's view presumably obscured, the Potters midfielder escaped punishment.
With the second half failing to maintain that lively start, the Citizens began to dominate possession as both Edin Dzeko and substitute Sergio Aguero went close with powerful efforts that fizzed just wide of the post.
As the game seemed to peter out with five minutes left to play, the deadlock was finally broken as, after City broke down the left, Aguero put the ball in, Dzeko managing to get a flick-on and divert it into the path of Pablo Zabaleta. The right-back, bursting into the area unmarked, hit home with the outside of his boot and Manchester City was finally ahead.
Cameron Jerome had the chance to level proceedings in injury time but spurned his chance, firing way over after the ball fell for him from a long-throw.