In a game of few chances Theo Archibald's stunning 25-yard volley settled the contest on 68 minutes, until which point Doncaster had held their own against Richie Wellens' side.
The visitors failed to register an effort on target, however. Top-scorer George Miller should have done better when he fired wide after being sent through on goal in the first half in their best chance.
Rovers remain one point outside the top seven but drop two places to tenth.
1. Match action
Doncaster's James Maxwell drives forward with the ball Photo: Howard Roe/AHPIX LTD
2. Jonathan Mitchell - 6
Made several smart stops and clearances to keep Orient at bay, particularly in the second period when the league leaders turned the screw. Will probably be disappointed with the goal, however. Photo: Gareth Williams/AHPIX LTD
3. Charlie Seaman - 6
Made some cracking passes to find teammates in space in the first half. Much less effective after the break though. Photo: Howard Roe/AHPIX LTD
4. Kyle Knoyle - 6
A steady display but again struggled to impact the game from an attacking perspective. Blazed a chance over the bar late on. Photo: Howard Roe/AHPIX LTD