David Mirfin's early own goal and Iain Hume's 39th-minute strike put Rovers in control but Mark Duffy reduced the Iron's arrears before the break.
Chris Brown restored the visitors' two-goal cushion three minutes into the second half before Karl Hawley scored to set up a tense finale, but Doncaster held on.
Rovers were in front after only five minutes when Mirfin turned a right-wing cross from David Cotterill into his own net at the far post.
Doncaster dominated for a spell with Hume and Rob Jones both going close to adding to their lead.
Brian Flynn's side did make it 2-0 when a Jones throughball from the half-way line split the home defence and Hume was left unchallenged to race into the box and pick his spot past on-loan Manchester City goalkeeper Eirik Holmen Johansen.
Two minutes later, Scunthorpe were thrown a lifeline when winger Duffy curled a 25-yard free-kick into the top right-hand corner of the net. But Rovers were back in command at the beginning of the second half when Brown finished off Hume's cross from close range.
Doncaster continued to dominate the second half without being able to add to their goal tally.
Scunthorpe scrambled a second goal in the 85th minute when striker Hawley claimed the final touch after a shot from Andy Barcham had come back off a post, but it was not enough to save them from a 10th home league defeat.