Five minutes before halftime, Huth earned the booking he should have received earlier, cautioned by Martin Atkinson for an ugly challenge on Micah Richards.
A scrappy start to the second half saw Stoke enjoy their best spell, but City’s defenders were more than equal to the challenge.
City again spurned a good chance on 56 minutes when a swift counterattack saw Tevez surge down the right before crossing to the unmarked Silva, who took too long to get his shot away.
With the clock ticking down, Mancini took the bold move to replace Gareth Barry with the more attacking option of Adam Johnson on 74 minutes.
A minute later, Toure struck the decisive blow for City. A shot from Balotelli deflected off Marc Wilson and fell kindly to the former Barcelona midfielder, who blasted an unstoppable first-time shot past Sorensen.