The much-changed Blues dominated the match pretty much from start to finish and established a commanding first-half lead thanks to goals from Sergio Aguero and Kelechi Iheanacho during an assured performance.
A late third from Kevin De Bruyne added gloss to the score line and completed an enjoyable afternoon in East Anglia and ended an arduous run of five out of the last six matches on the road.
Chasing silverware on four fronts would take its toll on any squad and it’s fair to say there have been times of late when the Blues have looked a little jaded.
It wasn’t lost on manager Manuel Pellegrini either, as he made seven changes to the team that started against Everton in midweek.
Iheanacho, Fernando, Pablo Zabaleta, Martin Demichelis, Jesus Navas, Raheem Sterling and Aleks Kolarov all returned for a tricky-looking third round tie at Carrow Road
...Norwich v City...
The changes meant there was a refreshing zip about City in the opening exchanges that saw an energy and verve that has been lacking somewhat of late.
Iheanacho looked lively and alert and it was the Nigerian striker who forced the first save of the game on eight minutes as he wriggled free in the box before seeing his shot pushed over by John Ruddy.
Captain for the day Kolarov fired in a long range effort two minutes later that was again pushed around the post by Ruddy as the Blues began to take a grip on the game.
City were inventive and totally bossing proceedings and on 16 minutes, the Blues were ahead with a goal that is as good as you’ll see all season
...Norwich 0 City 3...
Kolarov played a ball at pace into Sterling whose clever back-heel found Aguero and the mesmeric Argentine took over from there.
A good 30-yards from goal, he ghosted between two Norwich players before driving into the box, accelerating past Bassong and then poked the ball past Ruddy for a magnificent individual goal.
It was no more than City deserved and the pattern of play continued with Aguero again making Ruddy save well on 27 minutes, but when the second goal came, it was no real surprise.
Aguero was heavily involved again as he collected a long Delph pass before moving into the box and playing a simple pass to Iheanacho who made no mistake with a low drive to the right of Ruddy.
Two goals to the good at the break, City already had one foot in the fourth round and a number of players had already given the manager a timely reminder that this squad has plenty of options if and when they are needed.
Norwich, perhaps with an eye more on Premier League survival than a lengthy cup run, offered little in the way of a response and the Blues remained in control and largely untroubled after the break.
There was little in the way of goal-mouth action with the hosts subdued and largely outplayed and had Jesus Navas’ thunderous shot gone in and rather than rattling the bar on 75 minutes, it wouldn’t have flattered City – but within two minutes, the Blues did add a third goal to finally put the game to bed.
Substitute De Bruyne collected the ball, turned his marker inside out and then hit a low drive through Ruddy’s legs for his 11th goal of the campaign, much to the delight of the travelling City fans whose 400-mile round trip was starting to look like money well-spent.
There was still time for Bersant Celina to make his debut in the minutes that remained and the youngster from Kosovo twice went close in the final minutes.
All in all, a very satisfying day and a thoroughly deserved victory for the Blues whose twin drive for Wembley continues.
