The Whites fell behind in just the fourth minute as Mason Mount curled a fine finish into the top right corner from Chelsea's first attack.
United's task was then made even harder 20 minutes later as Dan James was shown a straight red card for a late challenge on Mateo Kovacic that eventually forced the midfielder off injured.
A dominant Blues side finally bagged a second goal ten minutes after the restart when Christian Pulisic applied a neat finish from the edge of the box and Romelu Lukaku bagged a third Chelsea goal with seven minutes left.
The result keeps Leeds in the relegation zone with just two games left.
Graham Smyth, the YEP's chief football writer, hands out the scores from another Whites defeat at Elland Road.
7. Kalvin Phillips
6 - Covered a huge distance, got stuck in but was guilty of a needless, rash foul that earned a yellow.
8. Lewis Bate
4 - The game looked too much for him. Overawed and outmuscled in the middle, found it hard to keep the ball.
9. Dan James
2 - Lost his head, rushed into a tackle that gave Taylor a choice to make and cost his team in the same manner Ayling did at Arsenal.
10. Jack Harrison
4 - Unable to impact the game in a meaningful way before he departed but was playing with an early knock.
11. Rodrigo
3 - Struggled to make a positive contribution, gave the ball away in dangerous areas.
12. Junior Firpo (sub)
5 - At least showed some attacking intent but could do little to stop Chelsea having their way with Leeds.