Sergio Aguero opened the scoring with just over half an hour gone and goals from Samir Nasri and Yaya Toure in the second half put City in complete control.
Even when Steve Morison scored a late consolation a 12th victory in 14 Premier League matches never looked in danger as substitutes Mario Balotelli and Adam Johnson boosted City's already impressive goal difference.
City have failed to score at least three goals on only three occasions in the league this season and they are now seven points clear at the top, although third placed Manchester United can cut the gap to five points with a win at Aston Villa in Saturday's late game.
Roberto Mancini's side were keen to make an early breakthrough and after a neat exchange of passes with Aguero, Edin Dzeko drove wide from just outside the area.
Norwich were the first team to really threaten after an error from Kolo Toure, making his first Premier League start since February, struggled to clear.
Morison managed to get a touch to Toure's failed clearance and then thumped a shot just wide of Joe Hart's goal.
Norwich's lone striker Morison went close again when confusion between Toure and Vincent Kompany at the back allowed the forward to break through, only to be denied by Joe Hart's brave block.
City were finally able to find some room in the area when Nasri's quick free kick put Aguero through but his firm effort was blocked at the near post by John Ruddy.
Aguero should have broken the deadlock when Nasri broke into the area and lifted a cross to the far post, only for the Argentina forward to shoot well over the bar from close range.
Dzeko was also denied when his clever flick took him away from Russell Martin only for Marc Tierney to throw himself in front of the Bosnian's shot.
But City finally broke through just after the half hour thanks to a moment of real quality from Aguero.
The forward was fed by a low cross from Micah Richards and spun in the area, despite having four defenders swarming around him, and stabbed into the bottom corner.
He could have added another shortly afterwards when he was picked out by Nasri once again but lifted his effort over the bar.
At the start of the second period City were almost caught out when Kyle Naughton's long ball forward was missed by Kompany and Morison but Elliott Bennett ran too wide to be able to find the empty net.
But City looked to have made the game safe five minutes after the interval when Nasri's crossed free kick was somehow allowed in by Ruddy.
The Norwich goalkeeper made up for that error with an impressive double save from Silva and Aguero as City continued to stream forward.
City extended their advantage further when Yaya Toure was picked out by David Silva's cross and clipped a shot into the corner from around 15 yards out.
Morison got some reward for his afternoon?s work when he headed in from David Fox?s cross with 10 minutes left.
But Balotelli restored the three-goal advantage when the ball went in deliberately off his right shoulder from close to the goal-line. And Johnson drove in a low effort in stoppage time to complete a convincing victory.