The Sky Blues, who were deducted 10 points this week for entering administration, scored after 13 minutes. John Fleck picked out Cyrus Christie with a tremendous cross-field pass before the full-back cut in from the right and fired a low, left-foot shot into the bottom corner of the net.
Home goalkeeper Joe Murphy had to be at his best to keep the scores level, however. Murphy showed fine reflexes to turn James Husband's deflected shot round a post in the 22nd minute before making two good saves to deny David Cotterill either side of half-time.
Rovers improved after the break. Dean Furman and Jamie McCombe both missed the target with volleys from close-range before Furman rattled a post with a 25-yard shot.
Coventry continued to put the pressure on and Christie hit the crossbar with a cross-cum-shot at the other end.
But Doncaster kept going and Furman headed over from close-range before Aaron Martin made an incredible goal-line clearance from a late Cotterill effort.