Nasri supplied the crosses for Dzeko to score his first two goals and he also played his part in the run-up to Sergio Aguero's strike, which made it 4-0 with half an hour to go.
Younes Kaboul headed home a consolation goal for Tottenham, who included Luka Modric in their line-up, but the afternoon belonged to Dzeko, who clinched his hat-trick by firing in from six yards on the hour before scoring his fourth - a beautiful curling effort - with the last kick of the match.
Two years ago Tottenham beat City to fourth place and the London side ran Mancini's men close for the majority of last season, but today's result was a clear indication of how much City have progressed over the last 12 months.
Described by Spurs boss Harry Redknapp as the best in the world, City outclassed the home side in every department, with Nasri and Dzeko the stars as City emphatically earned the result that maintains their 100% league record.
The result puts them top of the Premier League table - barring similar fireworks from Manchester United against Arsenal - having now scored 12 goals. Dzeko, who was ridiculed for parts of last season, has scored six of them.
For all City's dominance, it was Tottenham who started the brighter of the two teams.
Aaron Lennon and Niko Kranjcar both came close to breaking the deadlock in the opening few minutes and Joe Hart had to scramble to his left-hand post to prevent Rafael van der Vaart from scoring.
Nasri, Aguero and David Silva all looked dangerous on the attack for City though and Dzeko's physical presence as the target man kept Michael Dawson busy in the opening stages.
Former Gunner Nasri, whose every touch was booed by the home fans, sounded a warning to the home team when he skipped through the Spurs back line only for Kaboul to put in a crucial tackle.
Hart again had to scramble across his line to Van der Vaart on two occasions, but City were growing in confidence and Friedel pulled off a good save to tip Silva's goal-bound shot wide.
The game went into a bit of a lull before City opened the scoring in the 34th minute, with Nasri the architect.
The Frenchman played a tight one-two with Aguero before floating a ball across the box which Dzeko tapped past Friedel after beating Kaboul to the ball.
A block from Vincent Kompany and Joleon Lescott denied Van der Vaart before Crouch went within inches of equalising.
The England striker did well to get on the end of Gareth Bale's flat cross but his diving header sneaked just wide.
The towering striker was made to pay for the miss as Nasri raced up the other end and carefully picked out Dzeko at the back post and the former Wolfsburg man arched his back to nod the away side 2-0 up.
Silva went close to making it 3-0 in first-half injury time as Spurs ended the half very much on the back foot.
Redknapp sought to end City's dominance in midfield by replacing Kranjcar with the hulking figure of Tom Huddlestone and Defoe came on for Lennon soon after, with the England winger looking to have suffered an injury.
Dzeko came within inches of completing his first City hat-trick eight minutes after the break when he glanced a header just wide of Friedel's goal.
The Bosnia-Herzegovina international made amends almost immediately though when he got on the end of Yaya Toure's cross to rifle in to the roof of Friedel's goal for his sixth goal in four matches.
The home side's misery deepened just before the hour when Aguero brushed past Dawson's challenge in the box and clipped the ball over Friedel to make it 4-0.
Micah Richards came on for Zabaleta and Redknapp replaced Modric with Jake Livermore, much to the home crowd's disappointment.
Hart tipped over a brilliant effort from Jermain Defoe and the home side finally got themselves on the scoresheet from the resulting corner.
Kaboul lost Toure in the box and climbed well to head home Van der Vaart's corner to pull one back for Spurs.
Redknapp's troubles deepened 17 minutes from time when Van der Vaart walked down the tunnel with what appeared to be a hamstring injury.
Having used three substitutes, Spurs were forced to play the rest of the match with 10 men.
Dzeko was denied a fourth when Friedel saved the 25-year-old's close-range strike but his disappointment was short-lived.
The striker notched his final strike in injury time with the pick of the lot - a beautiful curler which beat Friedel at his far post to end a memorable afternoon for City and one to forget for Spurs.