League leaders make it seven wins from seven games at the Etihad Stadium despite a dogged defensive display from the Canaries, Toure, Johnson and Balotelli also netting
Roberto Mancini decided to line up with Sergio Aguero and Edin Dzeko up front, Mario Balotelli started from the bench after serving a suspension in mid-week.
City immediately impressed themselves on the game, Dzeko firing wide from 25 yards after being afforded too much space.
Steve Morison was playing in an isolated lone role up front for Norwich but still managed to cause Kolo Toure problems on a rare Premier League for the Ivorian.
First Toure dithered with a bouncing ball and Morison latched onto it, hitting an effort from 40 yards which sent Joe Hart scrambling to his right before a mix-up between both City centre-backs saw Morison through on Joe Hart's goal but a heavy touch from the striker let England's number on in to shut off the opportunity.
Roberto Mancini's men quickly re-established their dominance over the Canaries, Aguero jinked his way into the box, forcing a save from John Ruddy before Dzeko and Silva had efforts blocked in quick succession.
The game had swiftly become one-way stuff with City trying to pick holes in Norwich's side as they kept ten men behind the ball at all times, the creative trio of Sergio Aguero, David Silva and Samir Nasri sharing the creative duties.
Silva and Nasri combined down the right-hand side and the Frenchman's cutback found Aguero who could only fire over.
Dzeko had an effort blocked and the afternoon was threatening to become a frustrating one for City until they finally found a way through the wall of yellow shirts.
Nasri played the effervescent Micah Richards in down the right channel who played the ball into the box to Aguero who, faced with five Norwich players, turned into space and toe-poked the ball through the crowd and into the Norwich goal.
City were not happy to sit back on their goal, Toure powered through midfield and played Nasri in down the right who again found Aguero at the back post but the Argentine fired his effort over and could have easily had a first-half hat-trick.
Norwich managed to hold out until half-time and had a great chance to equalise in the second minute of the first-half, Kompany missed his header and Elliot Bennett found himself through on goal.
The former Brighton winger rounded Joe Hart but the angle became too narrow and Bennett could only fire wide.
City then extended their lead minutes later, City were awarded a free-kick on the left had side which was played in by Samir Nasri, the ball ending up in the back of the net after evading Norwich defenders and City attackers.
City were now fully into their attacking groove, Silva jinked into the box and hit a rasping effort towards John Ruddy's near post which was saved but fell to Aguero following up but he was denied brilliantly by Ruddy.
There was little rest for the former Everton stopper who was again sent scrambling by Gareth Barry's drive after a well worked short corner.
A change was needed for Norwich and Paul Lambert decided to take the game to the hosts, bringing on Grant Holt and Wes Hoolahan for Anthony Pilkington and Elliott Bennett, forcing a change of formation and perhaps style.
The change failed to have the desired effect however as another City short corner was worked by Aguero and Nasri into Yaya Toure who curled a sumptuous shot into the corner from 15 yards.
Roberto Mancini wasn't looking happy with just three, sending on Adam Johnson for Samir Nasri and one of the loudest cheers of the afternoon greeted Mario Balotelli as he replaced Aguero.
Norwich were still working hard however and were finally rewarded for their efforts, Surman's drfited cross was met by Morison, the Welshman powering a bullet header past Joe Hart.
City regained their three goal cushion through substitute Balotelli, played in by Johnson the Italian's initial shot was blocked into the air and as it fell the enigmatic forward hit the ball into the net with his shoulder.
And the Citizens extended their lead further in injury time, Vincent Kompany picking the ball up and finding Adam Johnson who slotted home from the right hand corner of the box.