The reigning champion fell to a 1-0 loss at Tottenham Hotspur in its opening game but had no trouble in seeing off its newly promoted opponent at Etihad Stadium.
British record signing Grealish scored in an unconventional manner 22 minutes into his home debut after Tim Krul's unfortunate own goal had given the hosts an early lead.
Aymeric Laporte added to the scoring in the second half and substitutes Raheem Sterling and Riyad Mahrez piled the misery on Norwich, which slipped to a second successive defeat on its return to the top tier.
City had won its previous three home league games against Norwich by an aggregate score of 14-1 and was ahead inside seven minutes of this one-sided encounter.
Gabriel Jesus chested down Rodri's diagonal pass and fired a low cross into the six-yard box, Grant Hanley diverting the ball against goalkeeper Krul and into the net.
Ferran Torres was denied a goal by VAR (video assistant referee) for Bernardo Silva's trip on Milot Rashica in the build-up, but Grealish netted soon after as Jesus's cross hit his thigh and beat Krul.
Having played a part in those opening two goals, Jesus went close to scoring one of his own early in the second half when dragging a shot just wide from range.
City's third did arrive nine minutes later when Laporte stroked home after Norwich failed to deal with a corner and the ball bounced around in the box.
Sterling was next to register with a close-range finish after being teed up by the impressive Jesus, while Mahrez rounded out the scoring late on, brilliantly controlling Ruben Dias's long pass and tucking in off the inside of the post.