Jerome, sent on as a second half substitute, proved to be the inspiration at a time when Blues were down to ten men after Fabrice Muamba had been sent off in the 57th minute.
His goal lifted all the tension which had previously existed and Seb Larsson sealed the game with a brilliant solo goal seven minutes from time when he outpaced four Wednesday defenders before scoring with a low cross shot.
The win took Blues back to the top of the Championship for the ninth time this season and to the verge of promotion.
The climax was in sharp contrast to Blues' ineffective opening 45 minutes when the likes of Larsson, Gary McSheffrey and Nicklas Bendtner were woefully out of touch.
But Wednesday, who suffered their first defeat in 12 games, were no better. Like Blues they failed miserably to create a single attempt on target in the first half.
There was certainly a keener edge about the second-half proceedings as Wednesday upped their game in an attempt to take fully advantage of a disappointing Blues side.
An indication of Blues' frustration came in the opening ten minutes of the second period when Muamba, Radhi Jaidi and Andy Cole were all booked.
They imploded in the 57th minute when Muamba received his second booking and was sent off for a strong tackle on Glenn Whelan.
This incident changed the whole complexion of the game as Wednesday suddenly realised that they had Blues on the back-foot but they too lacked the individual inspiration to take full advantage of Blues' situation.
Even referee Paul Taylor appeared to get carried away in the hectic battle when he mistakenly pulled out a red card for a booking against Richard Wood, only to quickly rectify his mistake by producing a yellow card.
Whelan and Kenny Lunt were sound workers for Wednesday in midfield, but the attack lacked the finishing power to penetrate Blues' defence in which Jaidi was their star performer.
Lunt emerged as their potential match-winner when he pounced on a loose ball in the 70th minute to hammer his shot against the crossbar with keeper Colin Doyle beaten.
But the game was transformed by the energetic play of Jerome who obviously upset Wednesday's defence with his enthusiasm.
He put Blues on the winning patch following a Larsson corner which was mis-handled by Chris Adamson and Jerome purposefully hooked the ball into the net to give Blues a crucial lead.
Larsson then sealed Blues' win when he raced through Wednesday's defence to produced a clinical finish.