Rovers were good value for the points after dominating the second half following a first period in which there was little to separate the sides.
Both sides produced some good football and cancelled each other out, although Rangers keeper Radek Cerny did well to save a free-kick from John Oster at full stretch in the 13th minute.
Visiting skipper Mikele Leigertwood went closest for Rangers with a 25-yard effort that curled just wide in the 24th minute, but it was a rare anxious moment for the resolute home defence.
Doncaster continued to press with Dean Shiels dribbling through to have a low shot saved from the edge of the box a couple of minutes later, before Cerny punched away a shot on the turn from Oster.
Doncaster had been unable to make the breakthrough despite edging the first half, but they redoubled their efforts when Rangers faded badly after the interval.
Billy Sharp lost his balance when presented with a good chance in the 48th minute and Shiels had another effort saved by Cerny in the 51st minute.
But the home side was not to be denied and they broke the deadlock in the 53rd minute when Rangers were caught badly napping following a corner from Quinton Fortune.
Fortune spotted Shiels unmarked at the near post and delivered the ball quickly to his feet with the winger crossing for Sharp to rattle home from close range.
There was no holding Doncaster after that and Shiels slammed home the second in the 65th minute after skipping past big defender Kaspars Gorkss on the edge of the box.
Rangers never looked like battling back and Rovers twice went close to adding to their score as they chalked up only their second win in 12 games.