Charlie Austin's second-half penalty all but confirmed Doncaster's relegation from the Championship as Burnley collected their third win in four matches.
Josh McQuoid opened his Burnley account with a 30-yard volley to put the Clarets ahead in the first half.
Doncaster drew level when subsitute James Coppinger crossed for Chris Brown to head home at the far post.
Adam Lockwood then bundled Danny Ings over and Austin buried the spot-kick.
Dean Saunders's side are now nine games without a win and are 11 points from safety at the foot of the table with four matches remaining.
Burnley remain in with a shout of making the play-offs, with Eddie Howe's men six points adrift of the top six and with trips to Leicester and Blackpool to come.
Ross Wallace was inches away from a spectacular early opener for the Clarets when his 30-yard effort swerved narrowly wide.
And McQuoid put the visitors ahead when he rifled an unstoppable effort into the top corner.
Saunders's men rallied after the break and were level when Coppinger's well-flighted cross was nodded home at the far post by Brown.
The winner came when Ings got goalside of Lockwood and was brought down.
Referee Nigel Miller had no option to point to the spot, from where Austin calmly converted.
Doncaster boss Dean Saunders: "We had a run of games Saturday, Tuesday, Friday and playing Leicester has finished a few of my players off.
"It's an accumulation of having tired on top of tired and having to scrap for points. Eventually something's got to give.
"We're not going to give up on survival. We don't need snookers yet but we're not far off. We've got four games left, but we've still got a chance of staying in the Championship - a slight chance."
Burnley boss Eddie Howe: "I thought we were excellent.
"First half we got into some great positions with some great counter-attacking football. We shot from distance an awful lot, much to my frustration on the sideline because I felt some of our decision making in the final third could have been better.
"I think if it was we'd have won by a more comfortable scoreline, but in the end it's a really good win."