David Moyes' unwanted records as Manchester United manager continued to tumble as rivals City eased to a 3-0 victory at Old Trafford.
Dzeko needed just 44 seconds to get on the scoresheet when he reacted quickest after Samir Nasri's effort came back off the post - the fastest goal at the Theatre of Dreams by an opposition player in the Premier League era.
The Bosnian doubled the lead on 56 minutes with an excellent volley from Nasri's corner, before Yaya Toure completed the rout in injury time.
Arsenal stumble while Everton cruise
- Arsenal 2-2 Swansea City
- Arsenal's nightmare continued as a bizarre own goal from Mathieu Flamini in the last minute handed Swansea a 2-2 draw at the Emirates Stadium.
- Gunners boss Arsene Wenger had called for a response to the "accident" of his side's 6-0 thrashing at Stamford Bridge which ruined his 1,000th match in charge on Saturday.
- Having trailed to an 11th-minute header from Wilfried Bony, it was not until the introduction of substitute Lukas Podolski just before the hour that Arsenal finally sparked into life with two goals in the space of 60 seconds which looked to have won the match.
- Newcastle United 0-3 Everton
- World Cup hopeful Ross Barkley scored one of the goals of the season as Everton continued their pursuit of the Barclays Premier League's top four.
- The England international stated his case eloquently in a 3-0 victory over Newcastle at St James' Park with a superb solo effort to remind Roy Hodgson of his blossoming talent.
- Team-mate Romelu Lukaku was just as clinical when he was presented with a chance to effectively kill the game off. Leon Osman cemented the victory with a third goal three minutes from time.
The defeat means United have lost 10 games in a single season for the first time since the Premier League's conception.
Further questions will surely be asked about Moyes' ability to bring the glory days back to United.
If anything, it was a minor miracle that City did not win by four or five.
David Silva, Toure, Fernandinho and Samir Nasri overran and outclassed a weak United midfield and Dzeko - a surprise starter ahead of Alvaro Negredo - did the rest up front.
It seems, after all, that Pellegrini had a point when he said there has been only one club in Manchester this year.
United lacked confidence, tempo and cohesion. There was no cutting edge up front while the back line was exposed for its lack of pace, just as was the case against Liverpool.
Moyes made life easy for the visitors too. Antonio Valencia was left on the bench and Adnan Januzaj did not even make the squad, leaving United with no width at all.
Moyes placed his faith in Tom Cleverley as has been common in the big games this year, and once again the England midfielder failed to deliver.
Things could have been worse had Marouane Fellaini received the red card he deserved for an elbow on Pablo Zabaleta or had David de Gea not prevented Dzeko scoring his third with a superb save.
There were plenty of glum faces by the final whistle, and one of them was Moyes'. The statistics do not make for good reading for the Scot.
United are now guaranteed to end the season with their lowest points total in Premier League history.
They have been defeated in six home games for the first time since 1978 and they have now lost three successive derbies for the first time in 45 years.
All the noises coming out of Old Trafford before the match were positive.
Sir Bobby Charlton said Moyes was "absolutely the right man" for the job.
Moyes wrote in his programme notes that it would not be long before United came through their "tricky period" and rose again.
The United boss said his team were not as far behind City in terms of quality as the table suggested, but that theory was shot to bits in the opening minute.
Toure sliced open the home defence to find Silva, who would have put City ahead had it not been for a decisive intervention from Rafael.
If United thought the trouble had passed then they were wrong. The cleared ball fell to Fernandinho, who found Nasri in acres of space in the box. The Frenchman's shot beat a stationary De Gea and the ball fell to Dzeko, who was left with the simplest of tap-ins.
Moyes sat there looking glum while the away fans proclaimed the Scot a "football genius".
For the rest of the opening quarter, United simply could not get hold of the ball. Silva penetrated the defence but fluffed his shot from 12 yards.
Dzeko slid the ball across the box, but Rafael was there to intercept again.
Silva snuck in behind the United back four again and squared for Dzeko, who placed his shot towards the bottom right-hand corner, but De Gea stuck out a hand and saved.
United fans, so supportive this season despite their team's failings, vented their anger as City's attack strolled towards the home defence unchallenged in attack after attack.
Joe Hart was twice called into action, but only to save weak shots from Wayne Rooney and Fellaini.
Fellaini then blotted his copy book by elbowing Zabaleta. He was lucky to get away with a booking.
United had one more chance before the break, but Rooney's fresh-air swipe from Rafael's simple pass summed up the hosts' first half.
Moyes brought on Shinji Kagawa for Cleverley at the break but it had no effect on the game.
Fernandinho headed over from six yards, but Dzeko made no such mistake soon after.
Fellaini blocked Rio Ferdinand's path as he tracked Dzeko and he was left unchallenged to head past De Gea.
United threatened momentarily through Welbeck, whose backheel was saved by Hart from point-blank range.
More substitutions came but nothing changed. Moyes sat in his seat dejected as Toure drove the ball beyond De Gea from 16 yards to wrap up the win in the final minute.
City move above Liverpool into second and three points off leaders Chelsea - but Manuel Pellegrini's men have two games in hand. United remain seventh, five points behind Tottenham.