David Moyes' men were buoyed by impressive wins over Olympiacos and West Ham heading into the contest but City stung them instantly as Edin Dzeko scored inside a minute to register the fastest away goal at Old Trafford in Premier League history.
United proceeded to stagger their way through the opening moments and rarely threatened to stop City extending their present dominance of the fixture to five wins from six league meetings, although Juan Mata might have levelled matters six minutes before the interval.
Dzeko finished precisely 11 minutes into the second half to give City breathing space and Yaya Toure added a third in the 90th minute, the Ivorian's fourth goal in two games.
Manuel Pellegrini's team are well-placed in the title race, three points behind leaders Chelsea with two games in hand ahead of Saturday's trip to Arsenal.
It is a battle Moyes and champions United must watch from afar, having won just one of 11 matches against the six teams above them in the standings this term.
Moyes selected a three-man central midfield in the hope of giving United a more robust feel but they suffered a nightmare start.
City immediately drove into opposition territory and Rafael was forced into a superb last-ditch tackle to deny David Silva, but his positioning was found wanting as Fernandinho worked the ball back into the left side of the area for Samir Nasri.
The playmaker thudded a strike against the base of the near post and Dzeko was on hand to tap home the rebound.
United struggled badly to gain an early foothold and Silva should have increased their anxiety when he scuffed a ninth-minute shot against a prone Rio Ferdinand - starting in place of the suspended Nemanja Vidic at centre-back.
Ferdinand appeared to be struggling with the pace of the game and carelessly played Silva onside in the 18th minute, leading to Dzeko drawing an excellent stop from David De Gea.
Marouane Fellaini drove into Joe Hart's gloves but the former Everton midfielder was perhaps fortunate to remain on the field with half an hour played after pushing his elbow into Pablo Zabaleta's face. Referee Michael Oliver decided a yellow card was sufficient.
United gradually worked their way into the half and Mata blasted over after Wayne Rooney’s 39th-minute air-shot.
Moyes sent on Shinji Kagawa for the ineffective Tom Cleverley at the start of the second half but City resumed on the front foot.
Fernandinho could not adjust to convert Vincent Kompany's flick-on from Nasri's 52nd-minute corner and headed over.
Yet United did not heed the warning and, when Nasri produced a similar delivery four minutes later, Dzeko coolly planted a side-foot volley beyond De Gea, ultimately sealing a ninth away league game unbeaten - a far cry from City's early-season troubles on the road.
The frenetic pace of the game subsided and Hart remained severely under-worked, with the exception of a sharp 71st-minute stop that kept out an impudent flick from England colleague Danny Welbeck.
A woeful evening for United was completed when a pass from substitute James Milner deflected into Toure's path, the midfielder driving home in trademark fashion.
