Debutant Samir Nasri, who quit Arsenal along with Cesc Fabregas to leave troubled Arsene Wenger scrambling for players late on in the transfer window, was the architect of the first two City goals with Dzeko expertly converting his crosses.
The Bosnia forward, anonymous last term after a big move from VfL Wolfsburg, sealed his hat-trick from close range after the break before strike partner Sergio Aguero scored a clever fourth and Younes Kaboul pulled one back.
Spurs, beaten to a Champions League spot by the visitors last term, had decent chances but the gulf in class was clear.
Chelsea target Luka Modric was booed by his own Spurs fans after his transfer request and their mood darkened further when Dzeko bent in his brilliant fourth in injury time.
In the other Sunday matches, striker Leon Best scored twice in Newcastle United's 2-1 home win over Fulham and Stoke City's Ryan Shotton struck late in a 1-0 victory at West Bromwich Albion.
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