Despite walking off with the matchball, Dzeko was denied a hat-trick after his breakaway effort on 67 minutes has been officially credited as an own-goal after the ball bounced off the post and the back of Norwich keeper Mark Bunn before rolling into the net.
Dzeko hopes his clinical performance against the Canaries will keep him in the starting line-up when Stoke come to Etihad Stadium on New Year's Day.
Edin Dzeko: "I didn't expect to play because it looked in training that I wouldn't. I was surprised before the game when the manager gave the team.
"Everyone wants to play, I was back and gave the maximum. Maybe it's important to score the first chance, it's different when you're winning 1-0 - maybe it's easier when you're a goal ahead and then we got the second soon after.
"We did it once before against West Brom, we played with ten men for 50 or 60 minutes - we did well and we did it again here - it was difficult, but we worked hard."
Source: Manchester City MAD