Kal Naismith's first-half penalty was enough to end a run of three games without a win for Luton, who beat top-six rivals Nottingham Forest 1-0 to push Fulham to the brink of the Premier League.
The Hatters defender tucked home a spot-kick after Jack Colback handled with 10 minutes remaining in the first half, which ended up being the only moment of the game.
Nathan Jones' side - who solidified their place in the play-off places with a win - were made to sweat in the final ten minutes after Sonny Bradley was sent off for a second bookable offence, but the Hatters held on for the win despite Philip Zinckernagel striking the post late on for Forest.
The result brings a run of five straight wins to an end for Steve Cooper's Forest, who failed to move within three points of second-placed Bournemouth ahead of their clash with Middlesbrough this afternoon, live on Sky Sports.
Meanwhile, Forest's defeat means Fulham's Premier League return will be rubber-stamped if they win at Derby later this evening at 8pm, with that fixture live on Sky Sports as well.
After a delayed kick-off by about ten minutes, the game burst into light under the Bedfordshire sunshine with chances going to both sides.
A brilliant ball over the top by Amari'i Bell found Fred Onyedinma in the penalty area but Bryce Samba got out well to meet the Hatters winger to tip his effort over the bar.
At the other end, Lewis Grabban - brought into the side over Zinckernagel - had a one-on-one chance saved down low by Luton's James Shea.
With eight minutes to go, the deadlock was finally broken when James Bree cut inside only for Colback to handle just inside the area, with referee James Linington taking his time to point to the spot.
And Luton put their penalty miss
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