For the second weekend running the Canaries found themselves 2-0 down at the break, with goals from Callum Reilly and Demarai Gray giving visitors Birmingham a flattering lead.
Norwich quickly got back on level terms thanks to a quick double strike from former Birmingham frontman Jerome. But, unlike at Cardiff last Saturday, they were unable to go on and claim the win.
The Canaries, having picked up 16 points from a possible 18 to briefly reach the Championship summit in midweek, took just eight seconds to get their first shot on goal.
Jerome’s effort was deflected harmlessly wide but the hosts looked a team full of confidence and Birmingham had a lucky escape after five minutes when Lewis Grabban volleyed Russell Martin’s cross well over from close range.
It look like being a long afternoon for the Blues, but completely against the run of play Birmingham took the lead from their first foray into Norwich territory.
Reilly’s low strike from the edge of the box had no venom in it but a deflection off Martin totally wrong-footed John Ruddy and trickled through his hands and into the back of the net.
The visitors then had what looked to be a decent shout for a penalty turned down when Martin appear to tug Clayton Donaldson back in the box.
Birmingham stretched their lead after 40 minutes when Gray kept his cool as the ball dropped kindly in the box and beat Ruddy with a neat finish into the far corner.
Alex Tettey should have pulled one back almost immediately but fired wastefully wide and an unsuccessful penalty appeal for a clear handball from Jonathan Grounds summed up a frustrating half for the home side.
Norwich needed a bright start to the second half and they got it, with Jerome reducing the arrears against his former club after 52 minutes.
Martin got to the byline on the right and his cross was swept home by the in-form forward.
Three minutes later it was all square as Jerome doubled his tally. This time the cross came from Redmond and a superbly timed header beat Randolph all ends up to make it six goals in five games from Jerome for his new club.
Ruddy then made a superb stop to keep out Donaldson’s near-post header as Birmingham looked to restore their lead, although the pressure on them soon started to build again.
The final chance came to Norwich defender Michael Turner but he directed a header just over in the dying minutes.