Early goals from Sergio Aguero and Dzeko put the visitors in front before Hull responded before half-time, only for Dzeko and Frank Lampard to earn their side the points in the second period.
The champions took the lead on seven minutes when Aguero took advantage of some slack home defending to angle a drive beyond Allan McGregor.
Just four minutes later, it was 2-0 when David Silva fed Dzeko and the Bosnian striker curled a thumping shot from the edge of the area over McGregor.
But Hull were helped back into the game on 21 minutes when Liam Rosenior powered down the right and his cross was headed into his own net by Eliaquim Mangala.
The summer signing from Porto then gave the home side the chance to equalise on 32 minutes when his high boot caught Abel Hernandez and the Hull striker converted the penalty.
Yaya Toure crashed a long-distance drive against the post early in the second half before the visitors regained the lead on 68 minutes when Dzeko rolled a low shot past McGregor.
Manuel Pellegrini’s side put the game to bed with three minutes to go when substitute Lampard was presented with a simple finish from Pablo Zabaleta’s pull-back.
The game began at a furious pace, Aguero charging at goal and testing McGregor at the near post with just 40 seconds on the clock.
Hull wasted little time making inroads of their own, Jake Livermore sending a devilish cross into the six-yard box where Nikica Jelavic just failed to make contact having slipped between Vincent Kompany and Mangala.
It took just seven minutes for the opener to arrive, Hull having twice failed to get the ball clear. Pablo Zabaleta battled hard to head back into the danger zone and Aguero needed just one touch to shoot across McGregor and into the corner.
Four minutes later Dzeko lashed in the second, collecting Silva’s pass and turning Rosenior before expertly finding the top corner.
Although early, it looked to be game over, as minds immediately turned to the visitors’ 7-0 thrashing of Sheffield Wednesday and whether it could be repeated. But Hull’s response was emphatic.
Gael Clichy, notionally supported by Silva, was an obvious target and was exposed as the hosts hit back in the 21st minute.
Ahmed Elmohamady linked well with Rosenior before the latter breezed past Clichy and crossed from the right. There were plenty of blue shirts on hand but the first, Mangala, lost his bearings completely as he sent an unstoppable header arrowing into his own net.
Aguero nearly dampened the celebrations when he went straight up the pitch and slotted an inch or two wide on the counter but Hull were not finished either.
Mohamed Diame began to boss the midfield, Toure and Fernandinho dropping deeper and deeper, while Elmohamady and Rosenior continued their assault on Clichy.
The reward came in the 32nd minute, Diame chipping to Hernandez only for the striker to be taken out by Mangala’s wild high-footed challenge.
The Uruguayan sent Willy Caballero, who had been selected ahead of Joe Hart, the wrong way and the champions were glad to hear the half-time whistle.
But the balance shifted again soon after the restart, Toure clattering the post from long distance.
Pellegrini’s men were back on the front foot, Silva re-emerging after a quiet period and Aguero always nagging.
But with the scores still tied the ineffective Fernandinho gave way for Jesus Navas for the last 25 minutes.
It was a risky switch that left Manchester City light on ball-winners but they regained the lead in a matter of minutes.
Silva was the driver, cutting inside and riding Diame’s challenge before freeing Dzeko on the left. The striker finished clinically, sliding his shot past the outstretched McGregor and in at the far post.
Hull had not given up, Gaston Ramirez working Caballero after stepping off the bench alongside Hatem Ben Arfa, and Tom Huddlestone seeing his 20-yard drive loop up off Kompany and over the crossbar.
But there was just enough time for Lampard to score his fourth goal in three games, arriving with a typical late run to convert Zabaleta’s cut-back.