Sharp, Bennett, James Coppinger and SimonGillett all had chances for Dean Saunders's side, while the visitors, who slipped down to 16th following the defeat, forced David Button into just one real save.
Birmingham started the brighter but Doncaster had the game's first chance when James Coppinger fired straight at Boaz Myhill and SimonGillett then dragged a shot wide after a mix-up in the Birmingham penalty area.
Tottenham teenager Ryan Mason, who signed on loan this week for a month, was among six changes to Rovers' starting line-up, with Shelton Martis, SimonGillett, Martin Woods, Sharp and skipper Brian Stock all returning.