Leeds had the game effectively wrapped up after half an hour in the Welsh capital as Patrick Bamford scrambled in a scrappy opening goal before Daniel James tapped in a second.
Cardiff goalkeeper Jak Alnwick made several saves to prevent the visitors from adding to their tally, while James struck the bar in the second half and Crysencio Summerville hit a post from his penalty.
Leeds eventually scored a third goal – which was still scant reflection of their vast superiority – as Georginio Rutter applied an emphatic finish to an incisive late counter-attack.
Daniel Farke’s side remain fourth in the Championship table, but stay within four points of Southampton in third place.
Cardiff, who were booed off by their fans at the final whistle, slip to 12th, but are still only three points adrift of the play-off spots.
Leeds needed victory to keep pace with the teams above them – and did so with a convincing display.
Farke’s men were quick to assert their authority, monopolising possession and barely giving their opponents a whiff of the ball.
Such was Leeds’ early dominance that, even after only 13 minutes, there was an air of inevitability about their opening goal.
The visitors carved Cardiff open on the left and Summerville fired a low cross which hit the sliding Bamford, bounced off Junior Firpo and back to Bamford, who poked in despite being sprawled on the ground.
Leeds’ second goal came from a similar position, with Cardiff’s Manolis Siopis giving possession away to Glen Kamara before Summerville’s shot was saved by Alnwick but only as far as James, who tapped in.
Cardiff’s keeper kept the score respectable as he denied Bamford and Rutter. But the one-sided nature of the contest prompted a smattering of jeers from the home crowd which became a fully-fledged chorus of boos by the time the half-time whistle blew.
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