After agreeing to defer half of this month's wages to help their cash-strapped club, Leeds' players could not be faulted for effort despite losing 2-1.
They have, however, now lost five of their past six games, conceding 18 goals, as the crisis surrounding the club deepens.
David Cotterill and Billy Sharp put Rovers two goals up in the first half but Leeds then raised their game and captain Ross McCormack nodded in his 28th goal of the season.
Rovers gave a debut to Australia defender Lucas Neill, who joined them this week on a month's loan from Watford, while Leeds brought back winger Cameron Stewart in place of Noel Hunt, who dropped to the bench.
Leeds fans staged a mini demonstration against owners, Gulf Finance House, after 20 minutes of the game by turning round and chanting: "Turn your backs on GFH".
Three minutes later Doncaster were ahead.
Cotterill's corner was headed out by defender Sam Byram to Robbie Wellens who laid the ball off for Cotterill to fire and angled shot past Jack Butland from 15 yards.
Leeds went close to an equaliser when McCormack's free-kick from the left sped inches outside the far post and Stewart's rising drive cleared the bar by a fraction.
However, Doncaster doubled their lead in first half time added on.
Byram failed to get the ball away from just inside the penalty box, leaving Sharp to plant the ball past the stranded Butland with ease.
Although Matt Smith and Tom Lees were unfortunate not to score just before the interval, Leeds made a double substitution at the start of the second half. Aidy White and Michael Tonge replaced Rudi Austin and Luke Murphy.
White, making his first home appearance since returning from a loan spell at Sheffield United, produced several determined sprints down the left as Leeds fans got behind their team again.
There were loud appeals for a penalty in the 58th minute as Doncaster's Leeds-born defender James Husband appeared to handle under pressure from Byram, but Leeds pulled a goal back four minutes later.
A free-kick was headed on by Smith for McCormack to head his fourth goal in as many games.
James Coppinger should have netted Rovers' third goal on 67 minutes but he spooned his hurried shot into the crowd after a mistake by Lees.
Leeds were a much more potent force since the substitutions and Rovers goalkeeper Johnstone was fortunate to escape with a yellow card when he brought down McCormack in full flight to the right of the penalty area.
After Jason Pearce had headed close, Stewart brought a swooping save from Johnstone as Leeds frantically sought an equaliser, Smith's header grazing the bar in time added on.