The final score from Colney was a 4-1 defeat.
Jacob Blackwell scored for City who travel to Birmingham on Tuesday in a re-arranged game in the 20th minute.
Norwich levelled in the 35th miute through Nick Davey and went ahead straight after the restart through Danny Kelly.
David Stephens side footed home a corner in the 72nd minute and Norwich completed their victory when Josh Dawkin curled a left footed shot into the roof of the net from 25 yards.