Harry Cornick gave Luton a surprise second-half lead before Stuart Dallas levelled from close range in 63rd minute.
The draw means Marcelo Bielsa's side go four points clear at the top of the Championship for now, but second-placed West Brom play Sheffield Wednesday on Wednesday evening.
A Jack Butland own goal and two from Kai Naismith saw Wigan secure a 3-0 win over Stoke, extending their unbeaten run to nine matches. Stoke are now just one point above the relegation zone.
Brentford comfortably saw off Reading 3-0 at the Madejski Stadium to keep their automatic promotion hopes alive thanks to goals form Bryan Mbuemo, Josh Dasilva and Joel Valencia.
Fulham, meanwhile, kept pace in the promotion hunt with Brentford by beating their other west London rivals QPR 2-1 at Loftus Road. Harry Arter and Cyrus Christie scored for the visitors after Jordan Hugill gave Rangers the lead in the opening minute.
Barnsley boosted their Championship survival hopes by beating 10-man play-off-chasing Blackburn Rovers at Oakwell. Conor Chaplin's header and a composed Jacob Brown finish proved enough.
Cardiff City, who occupy the final play-off spot in sixth, were held to a goalless draw at home by relegation-threatened Charlton Athletic.
Millwall drew 1-1 with Swansea at The Den which dents both their play-off hopes. Mason Bennett's 21st-minute opener was cancelled out by a Bartosz Białkowski own goal in the second half after the ball deflected off him from a Rhian Brewster free-kick.