Davide Somma came in for the suspended Bradley Johnson as United opted for a 4-4-2 formation.
But the Whites were being played off the park during the opening stages, unable to get the ball of Swansea.
So it was no surprise when Scott Sinclair dribbled his way through the Leeds defence to give the hosts the lead after 13 minutes.
United were unlucky not to be level by the break though after being denied a blatant penalty and hitting the woodwork.
It was 2-0 after 55 minutes when Max Gradel tripped Nathan Dyer and Sinclair converted the penalty.
Luke Moore added a third goal on 72 minutes.
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