The home sie kicked off attacking the River End goal and in the seventh minute Jamie Cureton set up strike partner Dion Dublin with a right-wing cross, but Neil Alexander superbly managed to turn Dublin's header round his right-hand upright.
Sylvain Legwinski was harshly booked for tripping Luke Chadwick after ten minutes and five minutes later Alexander was again in action, blocking a shot from Cureton, then diving on the ball before Dublin could tap in the rebound.
At the other end, Owen Garvan brought a smart save from Norwich keeper David Marshall following a quick Town break, with the former Celtic keeping doing well to palm the ball away.
Town's top scorer Alan Lee put the visitors ahead in the 27th minute when he slipped his marker on the edge of the box and beat Marshall low to his right, with a well-struck right-foot shot following excellent work from strike partner Pablo Counago to play the Irishman in.
Jason Shackell's header hit a post and was cleared, then Jamie Cureton, on this occasion not sporting a green and yellow hairdo, fired wide with only the keeper.
Town doubled their advantage shortly before half time, but the second goal was slightly controversial with some home fans thinking the ball had gone out of play when Billy Clarke hooked it across the face of goal for Pablo Counago to tap in from close range for his fifth of the season.
Former Colchester striker Cureton then somehow managed to fire wide with the goal at his mercy for what was easily one of the worst misses season in the Championship this season after a melee in the Town penalty area,
John Hartson replaced the injured Dion Dublin for the second half and nine minutes after coming on he won a corner on the City right. Martin Taylor raced to the near post unmarked to meet Simon Lappin's flag-kick and the ball flashed inside the near post off the head of Owen Garvan.
Eleven minutes later Cureton showed great composure when he put his earlier misses out of his mind to score with a cool chip with the outside of his right foot when Hartson headed the ball on into his path to bring the sides level.
Alexander, outstanding throughout the match was then forced to dive at full-stretch to deny the lively Hartson what would have been a winning goal for the home side.
Substitute Danny Haynes then had a chance to secure all three points for Town, following a break which led to a perfect cross from Alan Lee that Marshall managed to push onto the top of the crossbar and out for a corner kick.
With just minutes of injury time left to play, the hugely entertaining game ended on a slightly sour note when Darren Huckerby was sent off for a dangerous high footed tackle on Town winger Jonathan Walters that gave referee Rob Styles no option but to show the red card.
Town are still looking for their first away win of the season, and in truth were second best through most of the game, particuarly in the second half where Town's midfield were completely over-run by that of the homeside leaving on form strikers Pablo Counago and Alan Lee with little to no service.
The Blues were also far from convincing at the back with Norwich's first goal the result of poor marking and positioning from set pieces, something which has often blighted Town in recent years and will be surely something Town will look to resolve if the proposed takeover of Marcus Evans goes through.