The Latics, who have been a third-tier club for 21 consecutive years, have gone seven games without a win after creating few opportunities in a low-quality contest.
Doncaster captain Andy Butler headed an early chance over the bar, while Oldham striker Duckens Nazon was denied by visiting goalkeeper Ian Lawlor.
The best opening of the first half dropped to Doncaster top scorer John Marquis, but he fired narrowly over from the edge of the box.
Nazon went close twice in a matter of moments, first bringing a save from Lawlor and then drilling a second effort inches wide.
Another Butler header flew off target before Marquis teed up Ben Whiteman, whose shot from 12 yards failed to test home goalkeeper Johny Placide.
Oldham switched to a four-man attack as they sought the breakthrough, but the visitors held on with few problems and are unbeaten in five away matches.