United had been encouraged by wins over Olympiakos and West Ham United, but Dzeko needed only 43 seconds to put City ahead in the 150th league derby between the teams and the hosts never threatened to respond.
Dzeko claimed his second goal early in the second half before Yaya Toure added a late third to leave Manuel Pellegrini’s side three points behind leaders Chelsea, with two games in hand, ahead of Saturday’s trip to Arsenal.
The Bosnia international’s brace gave City a third consecutive victory at Old Trafford and prevented United from avenging their 4-1 humiliation at the Etihad Stadium in September.
Defeat left David Moyes’s United 12 points adrift of the top four and to compound matters, while they slumped to a sixth home defeat of the campaign, next week’s Champions League opponents Bayern Munich were beating Hertha Berlin to secure the Bundesliga title in record time.
Eager to avoid a repeat of United’s recent 3-0 loss at home to Liverpool, Moyes stiffened his midfield by deploying Tom Cleverley alongside Michael Carrick and Marouane Fellaini, but the hosts were behind within a minute.
After Rafael da Silva had thrown himself into a block to deny David Silva, City worked the ball wide to Samir Nasri on the left and when his shot came back off the near post, Dzeko tapped in.
Momentarily United looked dazed, and their sloppiness on the edge of their own box only invited City to attack them.
Jones had to slide in to block from Silva after Carrick lost the ball, while United goalkeeper David de Gea produced a superb one-handed save to thwart Dzeko and atone for a loose kick of his own.
– ‘The pride of Manchester’
Gradually the hosts began to make inroads, but City goalkeeper Joe Hart was able to save comfortably from first Wayne Rooney and then Fellaini, while Juan Mata lashed over from a Rafael cut-back.
Fellaini, meanwhile, was fortunate to make it to half-time after being shown only a yellow card by referee Michael Oliver despite appearing to catch City right-back Pablo Zabaleta with a deliberately raised elbow.
Moyes introduced Shinji Kagawa in place of Cleverley at half-time, but it was City who took the upper hand.
United were given warnings — Fernandinho heading over from an offside position, Jones producing a last-ditch tackle to deny Dzeko — but they did not heed them and in the 56th minute it was 2-0.
Nasri shaped a corner towards the near post from the right-hand side and Dzeko left Rio Ferdinand in his wake to steer a right-foot volley into the top-right corner.
With victory secure, City’s fans delved into their songbook, goading both Moyes and his predecessor, Alex Ferguson, as well as proclaiming their side “the pride of Manchester”.
There were opportunities for United to reduce the arrears in the latter stages, but Hart saved twice from England colleague Danny Welbeck and then boxed a deflected free-kick by Mata over the bar.
It was left to Toure to apply the coup de grace, collecting a deflected cross from substitute James Milner in the 90th minute and drilling a low shot into the bottom-left corner to notch his 21st goal of the season.