It could hardly have been more comfortable for Rovers as a jaded Orient side failed to land a single shot on target at the Keepmoat on Saturday.
Doncaster dominated the first half with David Cotterill and Chris Brown having shots well saved by overworked visiting keeper Jamie Jones before taking the lead in the 18th minute.
Cotterill flighted a corner from the right and player-coach Rob Jones charged through the penalty box to head home his seventh goal of the season.
Brown made it 2-0 with a well-taken goal in the 54th minute when he slid the ball through advancing keeper Jones' legs after beating the offside trap.
Orient's first serious attempt at goal did not come until the 65th minute when substitute David Mooney was wide of the mark, and they did not win a corner until nine minutes from time.
Doncaster could have scored more but Paul Quinn hit the post and Kyle Bennett had a shot headed off the line in the closing stages.