After Dean Ashton had given them the best possible start, blasting the ball past Gabor Kiraly in the sixth minute, the home side failed to press home their advantage and had to settle for a draw when Andrew Johnson poached an equaliser four minutes from half-time.
The home side kicked off and seemed to be on their way to an anticipated win in the sixth minute. Andy Hughes crossed from the right and Ashton's left-foot half-volley from 12 yards found the back of the net off the underside of the bar.
Ashton fired wide in the 23rd minute, then put in a low diagonal cross which was gathered by Kiraly before it reached Leon McKenzie.
Robert Green was at full stretch to keep out Jon Macken's shot in after 29 minutes and then, five minutes later, Macken limped off and was replaced by Wayne Andrews.
Kiraly was down smartly to keep out McKenzie's header before Darren Huckerby fired a foot wide from 20 yards, as the home side continued to dominate.
After Green had done well to save from Mikele Leigertwood, Huckerby lost possession in his own half and Johnson nipped in to score when he got a toe to Emmerson Boyce's low right wing cross to level the scores four minutes before the interval.
Norwich started the second half with Simon Charlton on for Adam Drury.
Kiraly saved well from McKenzie after he played a one-two with Huckerby, while the City defence had to block two shots from Johnson.
Ashton crashed a shot against the post while at the other end Johnson brought an acrobatic save from Green to ensure honours finished even.