Blues' problems are crystal clear as they have only scored six goals from their last eight games but they did extend their unbeaten home record to eight games.
Cameron Jerome gave them a first-half boost with an opportunist goal but Sammy Clingan earned Norwich a valuable point with a 53rd-minute equaliser.
Norwich, boosted by a large following of fans, are staging a desperate bid to avoid relegation and their latest performance gives them fresh hope of avoiding the drop.
They played with plenty of spirit and no small amount of skill to trouble a Blues side that is still not playing with the conviction expected of a second-in-the-table side.
With Scotland international striker Garry O'Connor making his first start since October 25th, Blues were expected to have extra fire-power up front but this was not the case in the early stages.
Skipper Gary Doherty was in complete control of the middle of the Canaries defence and as a result it was Norwich who posed more of an attacking threat than the home side.
Norwich, winners of three of their last four games, were certainly more positive and prepared to attack with Alan Gow, who had a fine game for the Canaries, firing just wide on one occasion with Blues' defence at panic stations.
On a very uneven playing surface the quality of play was not of a particularly high standard but Norwich were often the more dangerous with Gow popping up with one effort which went across the face of Blues' goal.
This situation produced a frustrating affair as Blues strived to gain the upper-hand against their lowly opponents but it was not until Hameur Bouazza's 35th-minute header that they recorded their first effort on goal.
They were malfunctioning badly and desperately required some inspiration which duly arrived in the 38th minute when David Marshall, challenged by Jerome, dropped the ball and the Blues striker turned to jab his shot home from a couple of yards from goal.
Norwich were back on level terms in the 53rd minute when their Northern Ireland international Clingan scored direct from a free-kick leaving his international colleague, Maik Taylor, transfixed on his line.
Blues took a long time to re-group as Norwich were given a big fillip by Clingan's goal which was a just reward for some persistent attacking play.
The first substitution was Scott Sinclair for Bouazza but there was little improvement in Blues' attacking play and this resulted in veteran striker Kevin Phillips being drafted into the game in place of the out-of-touch O'Connor.
In the last couple of minutes Marshall made amends for his earlier mistake with a fine save to keep out Phillips' header.