Carlos Tevez scored the only goal of the game which saw 12 minutes of extra time due to injuries sustained by Swans goalkeeper Michel Vorm, in his attempt to stop the Argentine's shot, and a knee injury to Micah Richards.
The goal came about just after the hour-mark when Tevez took possession and produced a strong run before firing into Vorm's bottom corner from 25 yards. The Dutch gloveman appeared to have strained something as he dived for the ball and required a stretcher to leave the field with Gerhard Tremmel his replacement.
With just over ten minutes of regular time remaining, it was Richards who need the aid of a stretcher after he went down clutching his knee with nobody else around.
Roberto Mancini's men would have felt very relieved to have come away with maximum points as they were well below their best whilst Michael Laudrup may rue taking nothing back to Wales, especially after Michu forced two vital saves from Joe Hart.
It was only the second time City had kept a clean sheet all season which is a positive but their all-round play was not as free-flowing as it was last campaign when they took all before them.
Nevertheless, the three points was recorded as City go second on the table whilst the Swans find themselves sitting 10th after their third defeat.
Etihad Stadium, Manchester - 46,801