Premier League: Hull 2 Man City 4
Winless in three league outings heading into the match, Manuel Pellegrini's men were simply irresistible during the opening stages at the KC Stadium as Sergio Aguero and Dzeko gave them a deserved 2-0 lead after 11 minute.
But Hull battled back relentlessly, overrunning their opponents in midfield and finding extended joy down the flanks.
Eliaquim Mangala, who so impressed on his Manchester City debut versus Chelsea last Sunday, was the main victim of Hull's ambition - the centre-back heading into his own net before fouling Abel Hernandez in the penalty area for the same player to level the contest in the 32nd minute from the spot.
Yaya Toure hit the upright with a brilliant long-range effort after half-time, leaving it to Dzeko - who netted twice in the 7-0 League Cup demolition of Sheffield Wednesday during midweek - to restore the champions' lead before Frank Lampard came off the bench to score for the fourth time in as many appearances for his new club.
Pellegrini made good on his midweek pledge to give Willy Caballero two games in row as the Manchester City goalkeeper kept his place ahead of Joe Hart following Wednesday's League Cup triumph.
Pablo Zabaleta returned at right-back after a red card against Chelsea, meaning the champions' only other change from that encounter was in the other full-back position - Gael Clichy replacing Aleksandar Kolarov.
Liam Rosenior came in for Stephen Quinn in the only change from Hull's last league outing at Newcastle, allowing Ahmed Elmohamady to revert to his favoured right-wing position.
Inside 40 seconds, Aguero sped past Hull centre-back Michael Dawson to unleash a fierce shot that was beaten away by Allan McGregor at his near post.
Hull should have led in the sixth minute as Nikica Jelavic, played on-side by Zabaleta and with plenty of room inside the Manchester City box, failed to make contact with Jake Livermore's measured cross.
And Hull were made to pay almost immediately. James Milner's right-wing cross was only partially cleared and Zabaleta was alert to nod towards Aguero, who rifled home on the turn.
It was soon 2-0 when Dzeko ghosted past Rosenior and curled a sumptuous 20-yard strike into the top corner.
Pellegrini's side appeared in rampant mood, but Hull had a lifeline in the 21st minute when Rosenior raced around the outside of Clichy and a poorly positioned Mangala headed his delivery beyond Caballero.
Dawson continued to endure a testing afternoon at Aguero's expense, the Argentina striker darting beyond his man once more to shoot narrowly wide.
But Hull were now in the ascendancy and Mangala had another moment to forget as he plunged a boot into Hernandez in the area, allowing the Uruguay defender to pick himself up and convert the resulting penalty after 32 minutes.
Hernandez and Dzeko passed up a headed opportunity apiece as a pulsating half reached its conclusion, with the visitors unquestionably happier to hear the whistle.
Caballero saved unconvincingly from Tom Huddlestone's early second-half drive before Mangala recovered his poise to deny Jelavic with a vital challenge.
Toure produced a nondescript opening period, but came to life to send a scorching 30-yard strike smashing into the post after 50 minutes.
Pellegrini replaced Fernandinho with Jesus Navas in the 66th minutes, allowing David Silva to operate in an advanced central position - a move that paid dividends three minutes later when the Spanish playmaker played in Dzeko to slot a left-footed finish past McGregor's despairing dive.
Caballero repaid his manager's faith with a sharp 86th-minute stop from Jelavic.
A minute later, Lampard continued a familiar purple patch in front of goal to make it 3-2 after fine work from Zabaleta, leaving Hull still without a Premier League win since the opening day.