United had to defend at the start but grabbed the lead when defender Scott Wootton scored on his debut in the 41st minute and they rarely looked back.
Billy Paynter did equalise two minutes after going on as a substitute but a powerful header from Matt Smith and a penalty from Ross McCormack sealed the tie in Brian McDermott's side's favour.
Both sides fielded full-strength line ups but it was Doncaster who took the game to their unbeaten rivals from the start.
Leeds had to survive an early scare as a result when Wootton came to the rescue to clear off the line in the second minute.
Richie Wellens and Chris Brown spliced the visitor's defence apart before the former took a return pass to beat Paddy Kenny with his shot only to see Wootton make a desperate clearance. Brown followed up but fired over the bar.
More incisive play from Rovers led to Dean Furman and David Cotterill linking to provide another chance for Wellens but he was unable to get any power behind his shot and Kenny made a comfortable save.
Doncaster worked tremendously hard to glue their opponents down and it was not until the 16th minute that Leeds created their first half chance.
A left-wing cross from Michael Tonge was punched out by keeper Ross Turnbull only as far as Ross McCormack who fired over the bar.
Leeds began to settle but they had Kenny to thank for not going behind in the 32nd minute when he dived full length to keep out a goal bound header from James Coppinger after James Husband had curled the ball over from the left.
Despite the home side having more of the play it was Leeds who snatched the lead in the 41st minute.
A cross from Tonge was headed back across the face of the goal by Smith to Wootton who headed home from point-blank range.
Rovers almost equalised immediately when Brown dribbled his way to the byline and flipped the ball across the six-yard box where Theo Robinson was waiting.
It only needed a tap to turn the ball into the net but somehow Robinson missed it completely.
Leeds began the second half as they had left off the first putting Rovers under plenty of pressure.
McCormack had an angled drive well saved and then Dominic Poleon fired into the side-netting.
But Rovers equalised against the run of play when a cross from Cotterill was headed home by Paynter in the 62nd minute.
United eased out after that, though.
A powerful header from Smith restored their lead in the 77th minute and McCormack added the third from the penalty spot three minutes later after Reece Wabara had brought down the speedy Poleon.