Dzeko added a second after the break with a cushioned volley from a corner, while Yaya Toure capped the result off with a low strike in stoppage time.
Here, Sports Mole takes an in-depth look at how City made it a derby double over their bitter rivals.
On target: 4
On target: 4
Was the result fair?
Yes. City began the match at a blistering pace and, for the first 15 minutes or so, United simply couldn't handle them. The hosts did eventually claw their way back into the match and even ended the first half on top, but that was their only spell in the ascendancy over the whole 90 minutes.
The stats make the encounter look more even than it actually was. From the moment Dzeko opened the scoring in the first minute, there was little doubt that City were going to go on and win the match. They controlled the tempo of the game and, with the exception of that spell at the end of the first half, looked remarkably comfortable throughout.
It may hurt United fans to hear it given their recent history of being the best, but they are simply not as good as City anymore. David Moyes will look for reasons why his side lost, but the most glaringly obvious of the lot was that City were just better the team.
Man Utd's performance
With the 3-0 defeat at home to Liverpool still fresh in the minds of United fans, this result will not do them any favours. They had appeared to turn a corner with back-to-back wins, but the simple fact is that they don't seem to perform against the big teams. They have still only managed one win against teams in the top nine all season.
Today's performance wasn't quite as bad as the one against Liverpool, but United were still second best and well beaten by a team that finished comfortably off their pace last season. They had their chances in the first half but never really looked capable of beating City.
They were blown away at the start of the match, but Moyes does deserve credit for tweaking his tactics to eventually stem the tide as City were dominating midfield. However, they failed to provide any real threat in the second half and eventually lost the match with a bit of a whimper.
Man City's performance
They came out of the blocks absolutely flying. Very rarely will they have started a match so quickly and United simply could not deal with them in the opening 15 minutes. The only negative about it was their failure to get a second goal, but that didn't prove to be costly in the end.
Pellegrini may not be happy about how his side allowed United to get back into the match, but that would only be a minor gripe, and one that was sorted out in the second half as City regained control and dictated the tempo of the game. Dzeko's second goal was the killer blow and from that point on the visitors never looked to be in danger of losing.
Indeed, they continued to look dangerous on the break and it speaks volumes that the third goal did not flatter them. It all seemed too easy at times, and such a comprehensive win will give them huge confidence for the rest of the title race.
Sports Mole's man of the match
David Silva: There were a number of City players in the running for this award. Fernandinho was instrumental in midfield, while Edin Dzeko more than justified his inclusion with a brace.
However, the award goes to David Silva for a majestic display in midfield, particularly in the opening stages of the match. As United struggled to come to terms with how well City had started, Silva pulled the strings and was at the heart of everything the visitors did.
The hosts could not get close to the Spaniard and, although he didn't register a goal or an assist, his general play was very impressive.
This one goes to Rio Ferdinand for his marking on City's second goal. The veteran defender was very slow to react to a fairly routine piece of movement from Dzeko, allowing the Bosnian striker to steal a yard that ultimately ended in a pivotal moment in the match.
Take nothing away from Dzeko as the finish was very impressive, but a player of Ferdinand's experience will be livid that he let the striker get away from him so easily.
Michael Oliver was a busy man tonight, especially in the first half. A number of his decisions were very clear, although looking back on his personal performance he will feel that he was perhaps too lenient on a couple of occasions.
Danny Welbeck lunged into a challenge on Pablo Zabaleta that earned him a yellow card which could have been a red, while Marouane Fellaini should have been sent off for a clear elbow on Zabaleta right in front of the ref.
Rooney also escaped a booking for a poor challenge at the end of the first half, leaving City feeling that Oliver wasn't being consistent enough with his decisions. All in all, there were a few small errors, but nothing major.
Man Utd: United will look to pick themselves up for another home match, this time against Aston Villa on Saturday.
Man City: The big games keep on coming for City, meanwhile, as they travel to North London to take on Arsenal, also on Saturday.