Danny Pugh volleyed home his second goal in successive games, leading goalscorer Ross McCormack struck with a brilliant overhead kick early in the second period and Tom Lees headed home in the 63rd minute.
Dean Saunders had registered two wins and a draw since replacing Sean O'Driscoll at the Keepmoat Stadium, but his side were no match for fast-improving Leeds, who moved into fifth place after stretching their unbeaten league run to five games.
Former Wrexham manager Saunders had lifted the gloom at Rovers with the help of a plasma television and a half share in a race horse as rewards for his players in training and matches.
But no incentives could make up for the gulf between these two sides in terms of cohesion and confidence and while Leeds manager Simon Grayson will be looking up the table, Saunders will now be aware of the full size of his task.
Former England goalkeeper Chris Kirkland, on loan from Wigan, and West Ham defender Herita Ilunga made their debuts for Doncaster, while a third new signing, Pascal Chimbonda, started on the bench.
Leeds were unchanged from the side that beat Portsmouth in their last match, with Finland internationals Mikael Forssell and Mika Vayrynen, as well as Luciano Becchio, named among the substitutes.
Doncaster threatened first after a cagey opening, with Jon Parkin's low shot forcing a sprawling save from Leeds goalkeeper Andy Lonergan.
Leeds responded with a swift counterattack, but Robert Snodgrass's driven cross was steered wide by McCormack.
Leeds soon began to boss possession and were rewarded with the breakthrough in the 20th minute when Pugh volleyed home in fine style, direct from a Snodgrass corner.
The home side were finding it difficult to get a foothold in the game and James Coppinger was booked by referee Kevin Friend after taking his frustrations out on Leeds midfielder Adam Clayton.
Parkin will feel he should have hit the target with a header from Coppinger's cross shortly before half-time, but Rovers failed to muster any real momentum and it was the visitors who looked the more likely to add a second goal.
Leeds sprayed the ball about with growing confidence after the restart and a moment of individual brilliance from McCormack doubled their lead in the 51st minute.
The Scot flicked the ball over his marker in the area and, with his back to goal, sent an overhead kick into Kirkland's top right-hand corner for his 10th goal in 13 appearances this season.
Saunders replaced Coppinger with Kyle Bennett in the 61st minute, but two minutes later Lees' thumping header from another Snodgrass corner put the result beyond doubt.
Lonergan was replaced by Paul Rachubka in the closing stages and Andy Keogh struck the crossbar with seven minutes left as Leeds threatened to add a fourth goal.