Hopes were high of another big-name scalp after victory over Southampton on Saturday, but the visitors proved too strong this time around.
There was no lack of endeavour from Les Parry's side, who were undone by a combination of clinical Leeds finishing and their own defensive short-comings.
Admittedly, the Rovers back-line won't face the likes of Jermaine Beckford and Gary McSheffrey too often at this level, but nevertheless Simon Grayson's side were given far too many gifts with which to punish the hosts.
Leeds were two goals up by the quarter-hour.
The deadlock was broken on nine minutes when Robert Snodgrass' free-kick found its way through a crowded penalty area to nestle inside the far corner, and just seven minutes later Jermaine Beckford had doubled his side's lead from the penalty spot after McSheffrey had glided unopposed into the danger area before being brought down.
Rovers hit back immediately when John Welsh netted at the near post to reduce the deficit, but it was 3-1 just after the half-hour.
Paul McLaren lost possession in the middle of the park and Leeds countered, Snodgrass picking out Beckford to cross for Luciano Becchio to finish with a diving header.
The game was over on 65 minutes. A long punt over the top was misjudged by the Rovers defence and Beckford raced onto the loose ball before finishing superbly over the stranded Luke Daniels.
Although disappointing, the next two games against Bristol Rovers and Hartlepool are likely to have a much greater bearing on the relegation dog-fight.