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.
13. Gjanni Alioski (sub)
8 - Added real quality. Claimed an assist and could have had another, if Costa had headed home his cross
14. Pablo Hernandez (sub)
8 - Some lovely passes. They didn't all work but he got Leeds moving forward again, with pace
15. Jamie Shackleton (sub)
N/A
16. John Brooks (referee)
7 - Missed little of consequence, no real controversy to be had.
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