However, the away team sealed the victory after the break as Dzeko and substitute Frank Lampard found the net to make sure of the points.
Here, Sports Mole takes a closer look at the action between the two sides.
On target: 5
On target: 6
Was the result fair?
Hull will feel unlucky not to come away with anything after fighting back from 0-2 down, but Manchester City earned a deserved victory in the end thanks to their added quality in attack. The mark of champions is to not give up and the Blues refused to let the match get away from them.
The hosts can take great pride from their spirited display as they had the champions worried on more than one occasion. To battle back from a two-goal deficit was impressive, though they eventually ran out of steam with limited options in attack. There was little in the way of creativity in midfield from the Tigers as Mohamed Diame, Tom Huddlestone and Jake Livermore were set up to stifle City.
Meanwhile, Hull's defence put up a brave fight despite conceding four goals. Steve Bruce's side have shown that they are capable of finding the net this season, scoring nine times in six games. All they have to do now is tighten up at the back and they will give anyone a run for their money.
Man City's performance
It was not always pretty from the visitors, but they got over the line in the end. From an attacking point of view it was what we're used to seeing from City as Edin Dzeko, Sergio Aguero and David Silva provided Hull with a constant threat in the final third. Silva in particular played a key role in many of his team's attacks, shifting position frequently so as to not let Hull get a grip on him.
However, City demonstrated yet again that they are susceptible in defence if teams get at them. The weak link on Saturday was Eliaquim Mangala, who looked like a different player following his impressive debut against Chelsea. Manuel Pellegrini will be the first to admit that his players are far from the finished article, though results like this will help to boost morale significantly.
Sports Mole's man of the match
Edin Dzeko: The Manchester City striker was a persistent threat for the visitors, moving well in the final third to give Hull countless problems. He took his first goal magnificently, smashing the ball into the top corner from the edge of the box. His second was more fortuitous, though it was pivotal in helping City claim the points.
Eliaquim Mangala had a nightmare spell during the first half, scoring an own goal and then giving away a penalty. For the latter he showed a complete lack of awareness inside the box by clumsily catching Abel Hernandez with his boot. Following on from his stellar debut against Chelsea, this was a day to forget for the French defender.
Anthony Taylor had a relatively quiet game, with little to report in terms of controversy. In fact, the official did well to allow both teams to play a free-flowing 90 minutes that was entertaining from start to finish.
Hull: The Tigers continue their Premier League campaign next Saturday at home to Crystal Palace.
Man City: The Blues return to Champions League action on Tuesday night when Roma visit the Etihad Stadium.