Billy Sharp scored twice as Rovers, down to the bare bones due to a lengthy injury list, ended a run of six games without a win to ease their relegation fears and consign Derby to a fifth consecutive home defeat and looking anxiously over their shoulders.
The Pride Park faithful reacted angrily to Clough's decision to bring off Theo Robinson just after Sharp's second goal, with chants of 'You don't know what you're doing' and the boos rang out as Joseph Mills added a third goal.
Steven Davies pulled a goal back right at the death but the damage had already been done.
Clough's side had the better of the first half but they were poor after the break and have now lost seven of their last eight at home.
On-loan Rams forward Jamie Ward came close with a right-foot strike from the edge of the penalty area after 13 minutes.
Derby had another chance to take the lead 36 minutes in when Miles Addison picked out Ben Davies at the back post, the midfielder controlled the ball with his chest but Rovers goalkeeper Gary Woods saved well with his feet.
Shaun Barker headed an inviting Ben Davies corner over from close range five minutes before the break, but moments later the Rams were caught napping as Doncaster took the lead with a goal that came out of the blue.
A long punt from Woods was not dealt with by the home defence and Sharp raced clear before firing clinically into the bottom-right corner with his right foot.
Woods did well to tip a Ben Davies free-kick over three minutes later and Steven Davies was off target with another excellent chance just before the end of a drab first half.
The Rams were unfortunate to be behind at the break but their was worse to come as Rovers doubled their lead two minutes after the break.
John Oster was the architect, jinking his way to the byline before standing a cross up to the far post where Sharp nodded home at the near post.
Rams boss Clough reacted by replacing Robinson, who scored the winner at Sheffield United on Saturday, with Bueno and the home fans voiced their disapproval.
Woods once again saved well with his feet to deny Ben Davies but the Rams were at sixes and sevens and Sharp should have completed his hat-trick when he raced clear after being picked out by Franck Moussa, but the diminutive strike dragged his left-foot finish wide.
The same pair combined once again in the 64th minute but Moussa's pinpoint cross was headed straight at Rams keeper Frank Fielding by Sharp.
Derby had totally lost their shape and Rovers cashed in 20 minutes from time when Mills surged forward and lashed a left-foot drive which Fielding got a hand to but failed to keep out.
Steven Davies pulled a goal back in the 90th minute with a neat close range finish but it was never going to be any more than a consolation.