A spectacular free-kick by David Beckham after just 95 seconds proved the difference in the 125th Manchester derby.
Beckham sent a stinging 30-yard set-piece into the back of the net, consigning Manchester City to a fourth successive league defeat.
Man Utd stayed top of the table on 33 points, five ahead of second-placed Arsenal. City were 16th on 14 points, four points above the bottom three.
Wayne Rooney scored twice as Manchester United came from behind to beat Sheffield United 2-1.
The Blades took a surprise lead through former Red Devil Keith Gillespie who headed in Derek Geary's cross after 13 minutes.
But two clinical goals either side of half time from Rooney was enough to sink the hosts at Bramall Lane.
The result left United at the top of the table on 34 points, three clear of Chelsea. Defeat for Sheffield United left them in the relegation zone, in 18th on 10 points.