Anything but a Derby win would have sent the Clarets back to the top flight, following their 1-0 win at Blackpool earlier on Good Friday, but goals from George Thorne and Chris Martin in each half prevented that.
Thorne’s 25-yarder at the end of the first half was barely deserved, but Derby were stronger after the break before Martin converted his 19th league goal of the season on 79 minutes.
Victory means the Rams, who were already assured of a play-off place before kick-off, kept their slim automatic promotion hopes alive with an eight-point gap behind Burnley with three games to go.
Defeat for Doncaster was their fourth in a row, a worrying trough in form with just a three-point buffer ahead of the drop zone.
Derby did not make a change from the team that beat Huddersfield 3-1 last time out while Doncaster were forced into replacing the injured James Husband with Enda Stevens. Lucas Neill (hamstring) and Richie Wellens (foot) did not pass their fitness tests.
Derby almost gifted Doncaster a fourth-minute lead following a near-calamitous mix-up between skipper Richard Keogh and goalkeeper Lee Grant.
Keogh had ushered a harmless ball into safety only to then wrong-foot his goalkeeper with a back-pass that Grant raced back to clear off the line.
Derby then spent the majority of a poor first half passing the ball neatly amongst themselves without creating any sort of alarm.
It was not the start that might have been expected of a side needing to win to retain hopes of automatic promotion.
Instead it was left to the relegation-threatened hosts to create the best openings, usually on the counter-attack, as fleet-footed wide men David Cotterill and James Coppinger intelligently ran into holes in the Rams backline.
Cotterill shot over from range when Patrick Bamford gave away the ball cheaply and Coppinger forced Craig Bryson into a tackle worth a caution after Sam Johnstone’s long throw caught out the Rams.
Doncaster worked Grant for the first time when Chris Brown powered a Gabriel Tamas cross on target that the goalkeeper tipped over.
Derby’s best moments had come from the flanks, but when Will Hughes was well placed, he wastefully over-hit a pass across the six-yard box.
But just as boss Steve McClaren would have been working out how to rally his side at the break, Thorne produced a stunning shot to open the scoring.
The ball was played back to him from the edge of the area by Hughes and the on-loan midfielder powered a side-footed shot into the left-hand corner and out of reach of the diving Johnstone.
It was his first Derby goal since joining on loan from West Brom in January.
Derby began the second half with more purpose as Andre Wisdom fizzed an angled drive wide before Bryson was sent clean through by a Thorne through-ball.
The prolific midfielder, who has 16 goals to his name this term, blasted his shot but Johnstone made a good low save.
Doncaster’s chances were limited after the break and Tamas needed to get more angle on his header from a Cotterill free-kick.
The gaps Doncaster enjoyed in the first half were not as easy to find, as Derby were happy to camp deeper and defend their lead, although when substitutes Mark Duffy and Theo Robinson combined Brown needed to be out quick to save with his chest.
The game was up on 79 minutes, though, as Derby finally found a second goal they had been threatening. Jamie Ward curled a cross to the far post for Martin to poke home with the outside of his right boot.
It was enough for the travelling fans behind the goal to find full voice, although their hopes of a return to the top flight for the first time since their disastrous 2007-08 campaign appears most likely to come via the play-offs.