The final scoreline flattered the visitors after Doncaster had dominated the second half and were denied an equaliser by a controversial late offside flag.
However, victory saw Leeds into sixth place in the Sky Bet Championship.
Leeds were the better side in the first half and grabbed the lead when big striker Matt Smith headed home a free-kick from Alex Mowatt in the 20th minute.
But Rovers battled back in tremendous style after the interval and were unlucky not to equalise when Theo Robinson fired home in the 66th minute only to have the effort disallowed for offside amid a storm of protest.
Leeds cashed in when Ross McCormack grabbed his 11th goal in the last seven games totally against the run of play in the 76th minute before Rodolph Austin rubbed salt into Rovers’ wounds with a third three minutes from time.
Both sides struggled in the windy conditions at the start and there was precious little football played in a frantic opening spell.
Doncaster were the first to threaten when Dean Furman had a 20-yard effort deflected into Paddy Kenny’s hands.
But when play settled down it was Leeds who began to assert themselves with Smith an imposing figure in attack.
Top scorer McCormack headed over the bar in the 17th minute after Smith had nodded the ball across the face of goal following a corner.
Furman brokered the next Leeds attack at the expense of a booking but the visitors snatched the lead from the resulting free kick in the 29th minute.
Teenager Mowatt, playing against his home-town club floated the ball into the box and Smith found the net with a stooping header from close range.
Ritchie Wellens had a goalbound shot deflected following a corner as Rovers tried to hit back but Leeds had the upper hand and Mowatt had a low shot saved in the 38th minute after Rovers had only half cleared a left- wing cross from Danny Pugh.
Rodolph Austin fired over the top after more Leeds pressure before Doncaster enjoyed a menacing spell just before the interval.
They had a great chance to equalise in the 44th minute after Robinson had brilliantly controlled a through ball from Wellens but he made a complete hash of the shot and fired high over the bar.
Smith headed over the top at the other end from McCormack’s right-wing cross to bring a hard-fought first half to an end.
Doncaster began the second half in a determined mood, pinning the visitors back in defence for long periods, and Wellens fired just wide in the 51st minute.
Wellens had another effort well saved five minutes later before Robinson’s shot was chalked off as the one-sided action continued.
Rovers were stunned when McCormack scored in opportunist style in virtually their first threatening moment of the second half before Austin added insult to injury from McCormack’s right-wing cross in the 87th minute.