A Carlos Tevez strike from 20 yards out sealed the points for Manchester City in the late kick-off.
Swansea's Michu had the games best chances, one in each half, but was denied each time by home keeper Joe Hart.
Tevez wrapped the game up on 61 minutes firing a low drive past Michel Vorm in the Swansea goal.
The game was marred by two serious injuries to Vorm and Machester City defender Micah Richards who were both stretchered off in the second half.
That led to twelve minutes of injury time and the longest game in Premier League history but Machester City easily held out to claim all three points.