City dominated the early stages and took the lead through David Silva from eight yards (12), before Sergio Aguero’s fine strike from an acute angle (48) put them two up and seemingly in control.
Anthony Martial then pulled one back from the spot (58), but the champions regained their two-goal advantage with four minutes remaining as sub Ilkay Gundogan controlled brilliantly and slotted home from close range after United fell asleep at the back.
The result means City go back to the top of the Premier League, two points above Liverpool and now four above Chelsea following their draw with Everton, while United are in eighth, seven points off the top four.
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