Blues registered a fifth successive Premier League win for the first time.
Birmingham went ahead on 12 minutes when Sebastian Larsson sent over a dangerous-looking cross.
Christian Benitez headed goalwards and the ball struck Liam Ridgewell before Jerome poked it over the line.
Birmingham doubled their lead on 48 minutes when Stephen Carr cut into the Rovers area before squaring the ball to Jerome, who fired in a low shot.
Ryan Nelsen gave Rovers a lifeline on 69 minutes. Pascal Chimbonda got on the end of Morten Gamst Pedersen’s free-kick and forced a good save out of Joe Hart but Nelsen was on hand to score.
With two minutes left Benitez hit the bar from close range but the miss didn’t matter.