Steve Howard fired a close-range shot at the post in the first half as the hosts sought a third straight win.
But Leeds responded, with Eddie Lewis curling a free-kick just wide and Michael Ricketts skewing his shot after being played in by Robbie Blake.
Clear-cut chances were few and far between though, and both keepers had relatively uneventful afternoons.
Leeds manager Kevin Blackwell:
"Luton have already rolled over two big names in Crystal Palace and Southampton and Leeds was the next big name on their list.
"We battled and you have to if you want to win the Championship.
"Half our team were playing together for only the second or third time and they will only get better."
Luton: Brill, Foley, Davies, Heikkinen, Underwood, Brkovic, Robinson, Nicholls, Morgan (Edwards 84), Howard, Feeney (Showunmi 77).
Subs Not Used: Perrett, Seremet, Holmes.
Booked: Howard.
Leeds: Bennett, Kelly, Butler, Gregan, Harding, Wright (Richardson 71), Bakke, Derry, Lewis, Blake (Healy 66), Ricketts (Einarsson 77).
Subs Not Used: Spring, Kilgallon.
Booked: Harding.
Att: 10,102
Ref: A Leake (Lancashire).