Jonathon Douglas opened the scoring, Jermaine Beckford netted his fifth goal in as many games, Argentine Luciano Becchio crowned an impressive display by scoring the third and substitute Enoch Showunmi added the fourth.
Both managers made a host of changes, suggesting the Carling Cup was well down their list of priorities.
Two of Palace's six changes were enforced, with James Scowcroft and former Leeds midfielder Shaun Derry suspended after their dismissals against Burnley.
United, who included just three players who started the league game at Yeovil, handed a debut to Leeds-born Aidan White and the 16-year-old had a solid game at left-back.
After stand-in keeper David Lucas made an early save from Palace striker Kieran Djilali, Neil Warnock's men conceded a soft goal in the 11th minute.
Beckford won a headed duel with Paddy McCarthy and Douglas could hardly miss from a few yards out.
Leeds were much the more impressive side and they doubled their lead on 32 minutes.
Neil Kilkenny played a free-kick into the box where Beckford's fierce shot was brilliantly turned around a post by keeper Darryl Flahavan but, From Kilkenny's corner, the striker rose to head home.
Beckford's striking partner Becchio showed some clever touches and from one neat turn he fired inches over the bar from an acute angle.
The Argentine was rewarded with the third goal in the 52nd minute.
He headed Frazer Richardson's cross so powerfully that Flahavan could only help the ball on to a post before it crossed the line.
Veteran Paul Telfer showed his wealth of experience, marshalling the Leeds defence superbly, and substitute Showunmi missed a simple chance before cutting in from the left to shoot into the far corner on 76 minutes.
Bradley Johnson's goalline clearance denied Calvin Andrew a consolation goal eight minutes from the end.