Samir Nasri was included in the City line-up for his debut following his ?24 million move from Arsenal and the France international responded with an outstanding display that included assists for three of the goals.
But even the former Arsenal midfielder was overshadowed by the performance of Bosnian forward Dzeko, who capped an impressive display with a remarkable display of predatory finishing.
Sergio Aguero was also on target for Roberto Mancini's side who are top of the table after scoring 12 goals in their opening three Premier League games, while Tottenham mustered a goal of scant consolation through Younes Kaboul's 67th minute header.
Tottenham have now conceded eight goals in two games, albeit against City and Manchester United, and their lack of strength in midfield was key.
Redknapp included Luka Modric in his team but the midfielder, a target for Chelsea ahead of Wednesday's transfer deadline, had little impact.
This was the first opportunity Mancini had to field highly-regarded quartet Nasri, Dzeko, Aguero and David Silva in the same line-up and they lived up to their billing.
City were accused of being dull and methodical last season but this year's model looks a very different prospect.
Within three minutes Tottenham winger Aaron Lennon had shot wide, but Mancini's men responded immediately with Nasri wasting a fifth minute chance to start his City career in spectacular style.
That set the tone for an open first half although Tottenham ultimately paid for their cavalier approach after failing to capitalise on their early strength.
Rafael van der Vaart came close with two excellent long range efforts, the second a curling free kick that had City keeper Joe Hart beaten, before Gareth Bale somehow spooned the ball over from close range.
It was City, though, who struck first, exposing the lack of cover for the Tottenham backline with Gael Clichy and Nasri finding it far too easy to work their way down the left hand flank before Nasri whipped over a low cross that was converted by Dzeko.
Spurs almost levelled when Peter Crouch headed wide from Bale's cross but having been breached once, the home side suddenly lost shape and conviction.
The second goal came in the 41st minute when Nasri again found space on the left and crossed towards Dzeko who again showed more determination than Kaboul to connect with a header that beat Brad Friedel.
The interval was reached with Spurs in ragged shape and any hope they had of clawing their way back into the game disappeared when Dzeko completed his hat-trick in the 55th minute.
Again, City worked their way through the Spurs defence with ease, this time with Yaya Toure finding his way to the byline before pulling back for Dzeko to complete his treble with a simple tap-in.
And the prospect of complete humiliation loomed for Harry Redknapp's side when Aguero collected Nasri's pass and rounded Michael Dawson for the fourth on the hour.
Tottenham at least responded when Kaboul met van der Vaart's corner with a powerful header.
But their miserable day was concluded when Dzeko scored again in stoppage time after Van der Vaart hobbled off with a hamstring problem with all three substitutes having already been used.
Source: AFP
Source: AFP