Burnley's 1-0 victory at Blackpool earlier this evening meant that the Rams had to win in Yorkshire to stand any chance of a top-two Championship finish.
A slip from Lee Grant nearly gifted Donny an early advantage, but the Derby keeper recovered to prevent Richard Keogh's back-pass from going in, and then saved well from Chris Brown's 22nd-minute header.
After the resumption of play, he kept out Bryson's powerful low shot to deny Derby a second and Thorne an assist, as it was his clever ball from the centre circle which had sent his captain through.
As the Rams became more dominant, Doncaster introduced Theo Robinson off the bench to increase their counter-attacking threat and the former Derby man almost equalised on 77 minutes.
He ran onto a chipped through-ball and looked to lift a shot over the outrushing Grant, who stretched out a hand to make a important block moments before his side doubled their lead.
It was Derby's own substitute, Jamie Ward, who had an impact on the scores as his cross to the back post was steered in smartly by Martin from six yards as Derby secured a third straight win.
They are now eight points behind Burnley with three games of the season remaining, while Doncaster sit three points above the drop zone ahead of their meeting with relegation rivals Millwall on Monday.