Goals by leading scorer Adam Boyd and substitute Jabo Ibehre in the closing nine minutes broke a stalemate to give Orient their first win in eight games.
Home striker Wayne Gray converted a 12th-minute penalty after he had been brought down by keeper Steve Phillips.
Rovers equalised when Rickie Lambert headed home a Stuart Campbell cross.
Both teams squandered further chances before Boyd restored Orient's lead with his 14th goal of the season and Ibehre then scrambled home a third.
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