There was nothing in the game for both sides, with City already securing second-place and Norwich returning to the Championship next season.
But that didn't stop City from putting on a rampant performance as they look towards their Champions League last-16 tie with Real Madrid.
Riyad Mahrez fired in a fourth before De Bruyne grabbed his second in the final minutes of the match.
It was David Silva's last Premier League appearance for City and he was given an emotional applause after being withdrawn in the second half.
Speaking after the game, Silva said: "It was emotional because they are amazing people, I have been working for them for 10 years and I have a good relationship with them. I love them and I am going to miss all of them.
"I am a lucky guy. I have had lot of nice moments, including this one as well - the last one."
City will host Real in Manchester on August, already ahead 2-1 after the first leg of their last-16 tie.