The England goalkeeper was dropped for the Premier League clash in favour of Costel Pantilimon, who ultimately had little to do as his outfield team-mates ran riot.
A Bradley Johnson own goal set the ball rolling, before further first-half efforts from David Silva, Matija Nastasic and Alvaro Negredo put the hosts firmly in control.
Yaya Toure, Sergio Aguero and Edin Dzeko added goals five, six and seven after the break as the match lived up to its goal-rich reputation, with 25 having been scored in the previous four top-flight meetings between the two sides.
In addition to the change in goalkeeper, Negredo replaced Javi Garcia in the only other alteration to the City side that started a 2-1 defeat at Chelsea last Sunday.
Chris Hughton also made a double change to his Norwich side from last weekend’s goalless draw with Cardiff City, bringing Johnson and Steven Whittaker in for injured duo Alexander Tettey and Robert Snodgrass.
The hosts dominated possession in the early stages, but they had to wait until the 15th minute for a clear goalscoring opportunity - Samir Nasri drifting into the area from the left before firing an effort against the outside of the post.
City had a slice of fortune as they broke the deadlock a minute later. Silva saw a shot blocked by Russell Martin in the penalty area, before an Aguero strike took a huge deflection off Johnson and looped over a stranded John Ruddy.
And City were two up within five minutes of going ahead, as Aguero cut the ball back for an advancing Silva, who made no mistake in sending a low drive beyond the Norwich goalkeeper.
The goals kept on coming for Manuel Pellegrini’s men with Nastasic the next to add his name to the scoresheet after 25 minutes - heading home from a corner via another significant deflection off Martin.
Negredo compounded Norwich’s misery 10 minutes before the break as he made it four from close range, although there were suspicions of offside against Aguero in the build-up.
Norwich finally gave Pantilimon something to do in the 38th minute, as the Romanian stopper got down well to touch Anthony Pilkington's effort wide of his post.
The half-time break provided some brief relief for Norwich, who were outclassed once again in the second period.
Toure curled in goal number five from a 20-yard free-kick on the hour mark as the match increasingly became a damage limitation operation for Hughton’s charges.
However, intent on causing even more carnage in the Norwich defence, Aguero added a sixth from the centre of the penalty area in the 71st minute, before Dzeko completed the rout four minutes from time from the edge of the box.
