Enzo Maresca made extensive changes to his starting XI, but City's squad depth was on full display as academy graduate Floyd Samba scored twice on his senior debut, while Allan Elias also found the net on his first appearance for the club.
• Manchester City: Floyd Samba 29', Rayan Cherki 32', Allan Elias 48', Floyd Samba 54', Ryan McAidoo 90'
• Norwich City: No goals
City took control of the contest in the 29th minute when 17-year-old Floyd Samba opened the scoring with a header. The academy graduate made an immediate impact on his senior debut, giving the hosts a deserved lead.
Just three minutes later, Rayan Cherki doubled City's advantage, putting the hosts 2-0 ahead before half-time.
Norwich faced an even greater challenge after the interval when Allan Elias scored in the 48th minute. The Brazilian winger marked his first appearance at the Etihad with an impressive finish to make it 3-0.
Samba then completed his dream debut in the 54th minute, scoring his second goal of the evening to make it 4-0. His brace highlighted the impact of City's academy players on a night when Maresca rotated his squad heavily.
City continued to dominate and added a fifth goal late in the match. Substitute Ryan McAidoo completed the scoring in the 90th minute to seal a comprehensive victory.
The result sends Manchester City into the Carabao Cup fourth round and provides further evidence of the depth available to Maresca. City made 10 changes from the side that defeated Manchester United 1-0 in the Premier League on Sunday, yet still produced a five-goal performance.
The victory also continues City's strong run of form across competitions. They had previously defeated FC Porto 2-0 in the Champions League and Manchester United 1-0 before returning to cup action against Norwich.
For Norwich, the defeat ended their Carabao Cup campaign, while City can now turn their attention back to Premier League action after another convincing victory.