Stephen Ireland grabbed the winner in the 78th minute after City keeper Nicky Weaver pulled off a string of first-half stops.
City escaped with just two minutes gone failing to close down Rob Hulse as Danny Webber picked out the big man, but United's leading scorer mis-kicked from 12 yards and Richard Dunne cleared.
Paddy Kenny found Hatem Trabelsi's teasing cross too hot to handle, punching clear before the United keeper was almost beaten on 13 minutes. Ousmane Dabo ran on to a loose ball to lash in a stinging shot from 30 yards, the ball bobbled and hit the keeper on the shoulder before Kenny charged to smother the ball under Bernardo Corradi's challenge.
City escaped as United looked for the early breakthrough, centre-back Claude Davis drilling a low shot into the packed area as Micah Richards appeared to use both hands to push the ball away under the nose of referee Mark Clattenburg.
Weaver pulled off a stunning save from Stephen Quinn, the little midfielder twisting past two players, his left-foot strike tipped round the woodwork by the diving keeper.
The acrobatic Weaver foiled Phil Jagielka with an even better stop, this time diving to his right to push the blonde-haired midfielder's powerful right-foot strike round the foot of the post, before United had an amazing let-off after Mr Clattenburg failed to spot another clear hand ball.
Joey Barton, hoping to win an appeal after his sending-off against Bolton at the weekend, whipped in a corner from the left, Micah Richards headed back into the area and full-back Rob Kozluk scooped the ball off the line, under pressure from Darius Vassell.
Georgios Samaras replaced the ineffective Corradi and was handed a chance on 55 minutes the big striker steaming in after a mistake by Davis only to drill his angled drive wide of the far post.
Dunne cut out a low cross from substitute Chris Armstrong and Richards stretched to head a Keith Gillespie inswinging corner from under the bar as United piled forward.
Webber almost found a way through getting a touch to a Gillespie cross as Weaver pulled off another brave stop at the foot of the post.
City broke the deadlock in the 78th minute, Trabelsi's curling cross from the right was coolly chested down by Samaras into the path of Ireland, who struck a low shot from just outside the area beyond the diving Kenny.