It was Birmingham's first home win of the season but they made hard work of their task before Jarosik, on loan from Chelsea, hammered in a 25-yard blockbuster into the roof of the net.
Norwich, in free-fall in the Championship, were looking to Darren Huckerby and Dean Ashton to spark off a revival.
It was not forthcoming in the opening 30 minutes but they engineered a fighting comeback when the inconsistencies of the Birmingham side again came quickly to the surface.
There was an obvious determination about Birmingham at the start as Norwich found themselves under the hammer as the Midlands club took complete control in this spell.
Unlike in their previous home games Birmingham did not find themselves chasing the game. On this occasion they were able to build up an early lead which made a major difference to their performance but they were guilty of some slack play which enabled Norwich to stage a recovery.
Ominously for Norwich and their leaky defence they found themselves in arrears after only five minutes as a result of a goal scored direct from a free-kick by Jermaine Pennant.
Gary Doherty conceded the foul when he brought down Mikael Forssell and Pennant fired a high shot which was agonisingly deflected by a Norwich defender past the unfortunate Robert Green.
Some five minutes later Pennant took another free-kick from almost the same position but on this occasion Green was able to flick the former Arsenal player's shot over the bar.
The Canaries were certainly not on song at this point in the game despite the fine support of some 3,000 travelling fans.
Manager Nigel Worthington's problems were plainly evident as Norwich as they struggled to gain control of the midfield.
With Nicky Butt enjoying one of his better games for Birmingham the Premiership club were able to dictate most of the play but went off the boil and allowed Norwich to get back into the game in the 41st minute.
A long ball out of defence found Ashton tracking down the right. Matthew Upson closed in but mistimed his tackle and finished up sliding into the advertising boards.
Ashton carried on and fired in a shot from a narrow angle which took a deflection off Martin Taylor to go out of the reach of Nico Vaesen and into the far corner of the net.
But Birmingham should have regained the lead in the 43rd minute when Emile Heskey was brought down by Jim Brennan only for Forssell to hammer his spot-kick wide of the post.
Norwich were boosted by these incidents and only a goalline save by Vaesen, making his first appearance of the season, prevented Ashton giving the Canaries the lead a minute into second half.
Heskey made way for Walter Pandiani but it was Jarosik who raised Birmingham's spirits with a long-range swerving shot which smashed against the post.
With the game heading towards extra-time Jarosik delighted the home fans when he finally got a shot on target with his late winner.