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.
1. Illan Meslier
6 - Beaten by a wonderstrike, flapped at a free-kick but was brave and decisive to foil a Cornick breakaway
2. Luke Ayling
7 - Solid if unspectacular. Struggled to find men in the first half, but options ahead of him were few and far between
3. Liam Cooper
NA - Injured after just 12 minutes. Tried to walk it off but looked in considerable pain
4. Ben White
7 - Looked comfortable for the most part. Appeared to have tracked Cornick but couldn't get close enough to stop the shot that brought the goal.
6. Kalvin Phillips
7 - Set-pieces were largely poor but put in some good tackles and kept the ball moving.