Sean O'Driscoll's team have earned praise for their classy football in the past, but this was more of a battling display.
Swindon fought hard but lacked menace in front of goal and had defender Hasney Aljofree sent off to add to their misery.
Rovers made five changes to their starting line-up and had three key defenders missing through injury and suspension, but shoddy Swindon failed to cash in and seldom posed a threat.
Town battled hard but lacked ideas and flair and Doncaster matched them for work-rate before applying the killer punch.
Lewis Guy had a fierce volley instinctively parried by visiting keeper Petr Brezovan, before Doncaster snatched the lead just before the interval.
Gareth Taylor produced a superb throughball for Sean McDaid to sprint clear and slot home his first league goal for the club in fine style.
It had been scrappy for most of the half but Brain Stock almost pulled off a moment of quality a couple of minutes later when he spotted Brezovan off his line and, from near the halfway line, hammered a long-range shot which missed by inches.
There was a rare chance for Swindon in the 58th minute when Steve Roberts made a hash of a clearance and gifted the ball to Billy Paynter, but his shot was brilliantly saved by Neil Sullivan.
Stock slotted home the second goal from the penalty spot after 68 minutes after Aljofree was sent off for bringing down Mark McCammon.
Swindon had a couple of chances in the closing stages as Rovers seemed to settle for their two-goal advantage, but the visitors made a hash of them both.
Substitute Andy Nicholas failed to connect cleanly with the goal at his mercy in the 81st minute and Paynter fired straight at Sullivan four minutes from time.