United lost skipper Liam Cooper to injury inside seven minutes and Luton took a shock lead through substitute Harry Cornick five minutes after the break.
Leeds drew level three minutes after the hour through Stuart Dallas but the Whites could not find a winner. YEP chief football writer Graham Smyth hands out the scores.
7. Mateusz Klich
6 - Ran a lot but couldn't link the defence and the attack in the first half, withdrawn on the hour mark.
8. Helder Costa
6 - Saw lots of the ball but struggled to provide much end product. Dribbled the ball well. Effort was there.
9. Jack Harrison
7 - Far more involved in the second half, posed a real threat on the left and never stopped running
10. Tyler Roberts
6 - Struggled to find space to work in the first half, couldn't get free to give defenders options. More involved in the second half
11. Patrick Bamford
5 - Failed to impact the game. Couldn't provide an outlet in the first half, couldn't take advantage of a terrific cross for his best chance of the game
12. Gaetano Berardi (sub)
6 - The substitute was substituted. Had one rocky moment but was otherwise solid