The goal, which came against the run of play, seemed to galvanise Birmingham and they were unlucky not to be awarded a penalty after Clayton Donaldson was pulled back by Martin in the box.
A David Davis drive from range was then tipped around the post by Ruddy as the visitors looked to extend their advantage.
They eventually got a second after the Norwich defence failed to clear on the edge of the box, allowing Gray to curl a fine shot beyond Ruddy.
The hosts came out rejuvenated after the break, and Jerome clawed a goal back for them with a superb first-time finish into the bottom corner.
The dramatic start to the half then saw Norwich pull level after Jerome rose above Paul Robinson to loop a header home.
Birmingham were shellshocked by Norwich's fightback, but almost got back in the lead through Donaldson, but his disappointing header from close range was straight at Ruddy.