The Canaries were on top in the first half and were unlucky to be a goal down at the break.
After equalising early in the second half, the game became more even although Birmingham could have snatched victory in the closing stages if David Marshall had not pulled off a brilliant reflex save to deny Kevin Phillips.
Birmingham kicked off attacking the River End goal and Phillips tested Marshall early on with a long-range shot.
In the tenth minute Darel Russell was denied a shooting chance when Maik Taylor moved smartly to clear the ball for a corner.
Arturo Lupoli went down dramatically in the penalty area, but the referee was unimpressed.
The home side continued to apply most of the pressure without producing a clear-cut shooting chance.
In the 26th minute Lupoli's shot hit the side-netting and for the next ten minutes the Canaries looked to be much the better side.
In the 38th minute Norwich did get a shot on target, but Taylor made a comfortable save from Mark Fotheringham's free-kick.
Within two minutes James McFadden's free-kick from the Birmingham right was headed home by Sebastian Larsson beating Marshall to his left, to give the Blues an unlikely half-time lead.
Within seconds of the re-start Norwich equalised, when a determined run down the Norwich left by Lupoli, set up Russell whose left-foot shot from ten yards beat Taylor low to his left.
From that point the game became much more even than the first half, but neither side came close to scoring until Jon Otsemobor's volleyed right-wing cross was headed over by substitute Jamie Cureton.
Russell's shot was saved by Taylor and, at the other end, Blues' substitute Gary McSheffrey fired over with only Marshall to beat, before the Norwich keeper kept out Phillips' shot to earn his side a deserved point.