It was a tough battle between two in-form sides but Doncaster - beaten just twice in their last 21 games - always had the edge.
They set the pace at the start with Brian Stock and Richie Wellens in command in midfield and they almost snatched the lead in the sixth minute.
Mark McCammon and Jason Price combined to set up a chance for James Coppinger, whose angled shot was cleared off the line by visiting skipper Stuart Campbell.
Bristol keeper Steve Phillips was badly shaken by a challenge from McCammon in the tenth minute which left him prostrate and the big Doncaster striker was booked although it looked as if he had every right to go for a 50/50 ball.
Phillips played on after receiving treatment and the game became disjointed for a spell with a number of interruptions as the trainers came on to treat injuries.
But the home side regained their grip with Price firing over the top from close range in the 22nd minute flowering good work by McCammon and Coppinger.
Chris Lines had a header saved by Neil Sullivan when Rovers began to press just before the interval, but Doncaster resumed on the attack in the second half with Price missing a great chance when he headed over after being left unmarked at a corner.
Price was desperately unlucky four minutes later when he sent a great header goalwards after latching onto a cross from Wellens but the ball rebounded off the post.
Doncaster finally made the breakthrough they deserved in the 65th minute when Wellens was brought down by Aaron Lescott and Stock sent Phillips the wrong way with the resulting penalty.
Andy Williams went close with a glancing header before substitute Paul Heffernan wrapped up the points for Doncaster when he slammed home another penalty in injury-time after Anthony Pulis had handled a free-kick from Stock.