Steve Bruce decided to play Jerome alongside Mikael Forssell and the pairing paid off after only 32 seconds when City took the lead.
Derby were outplayed in the first half but came back to equalise through Matt Oakley before another clinical finish from Jerome won it.
There were boos from the home fans at the end but Derby could not be faulted for effort and commitment although they used the ball poorly at times.
Birmingham should have won the match before half-time and they could have paid the price when Derby came at them in the second half but overall, they were better than last season's Championship rivals.
The central midfield pairing of Johan Djourou and Fabrice Muamba was at the heart of their success although they also had to defend strongly after the break.
Derby had been caught cold at Spurs last week and they were floored in the first minute when Forssell slipped the ball between Andy Griffin and Andy Todd for Jerome to slide a low finish past Stephen Bywater at his near post.
If there were question marks over the keeper for the goal, he kept his side in it with two superb saves to deny first Forssell, when the striker appeared to have gone round him and then Muamba, when Gary McSheffrey put the midfielder through.
Radhi Jaidi also struck the underside of the bar and Derby were relieved to go in only one goal down.
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Derby began to push City back but the visitors regained their composure and went back in front with a superb goal in the 63rd minute.
Stephen Kelly crossed from the right, McSheffrey flicked the ball on and Jerome showed great balance and skill to send a right-foot shot past Bywater.
Derby kept plugging away but, Teale apart, they did not carry a real threat and too many passes failed to find their target.
Even so, they might have equalised again in the final minutes when Oakley fired in a low shot from the edge of the area which Taylor kept out diving low to his right.