Substitute Craig Bellamy set up all three goals as Blackburn eased into the last 16 of the Carling Cup.
Rovers dominated from the start and Brett Emerton, Paul Dickov and Shefki Kuqi all went close in the first half.
The dogged Leeds defence was finally breached when Bellamy found Brett Emerton who shot home from 12 yards.
Close-range strikes from Dickov and Lucas Neill sealed the win while Leeds had Gylfi Einarsson sent off for a two-footed lunge on Robbie Savage.
Bellamy came off the bench and provided the sort of impact that persuaded manager Mark Hughes to part with £5m in the summer.
A knee injury has blighted the Welsh international's early Rovers career since his move from Newcastle and he has been limited to just five senior starts.
But within eight minutes he had unlocked the Leeds rearguard, a delicate pass setting Emerton free to score with the help of a deflection off Matthew Kilgallon.
And Bellamy went on to tee up Dickov with a drilled cross from the left, before providing Neill with an inch-perfect pass to score the third.
Hughes sent out a full-strength side, and while they failed to fire in the first half Blackburn deserved their win against a limited Leeds side who failed to test Brad Friedel in the home goal.
Neill scored after the visitors had been reduced to 10 men following Einarsson's red card - a decision his manager Kevin Blackwell described as "rubbish".
Blackburn boss Mark Hughes:
"He has so much quality in the attacking third and generally has an impact when he comes on, which he has done again here.
"We have to get him playing regularly and he is not far from full fitness.
"I want to progress in this competition and think it is better to start with your strongest side."
Leeds boss Kevin Blackburn on Einarsson's red card:
"I have seen the video and both players had their feet off the ground.
"To be fair, they both went for the ball but if you send one off, you have to send both off.
"Savage clearly wasn't badly hurt, but then we are not in the Premier League. I don't know if we will appeal."
Blackburn: Friedel, Neill, Todd, Khizanishvili (Mokoena 68), Gray, Emerton, Savage, Tugay, Pedersen, Kuqi (Bellamy 53), Dickov (Jansen 78).
Subs Not Used: Enckelman, Bentley.
Booked: Emerton, Tugay.
Goals: Emerton 60, Dickov 76, Neill 89.
Leeds: Sullivan, Richardson, Butler, Kilgallon, Harding, Moore, Einarsson, Gregan (Douglas 70), Pugh (Lewis 72), Healy, Blake (Hulse 77).
Subs Not Used: Bennett, Walton.
Sent Off: Einarsson (86).
Ref: C Foy (Merseyside).