The Hatters missed several chances before Steven Howard headed them in front, only to see Andy Johnson reply for Palace early in the second half.
But Luton kept their nerve and Ahmet Brkovic gave them victory 11 minutes from time.
A stop-start first half got more interesting as the game progressed. Apart from a free header from Mark Hudson, Palace offered little while Luton looked more lively in the early stages.
The visitors should have gone ahead after 23 minutes, when Hudson pulled back Steve Robinson for referee Phil Dowd to award a penalty. But skipper Kevin Nicholls saw his penalty saved by Gabor Kiraly - the Hungarian keeper guessing right and diving to his left to keep out the poorly struck effort.
But Luton did not let up and Kiraly rescued Palace again to prevent Brkovic from scoring, before Warren Feeney shot wide from just five yards out.
The Hatters were eventually rewarded for their useful first-half endeavours, when Nicholls hoisted over a free-kick from the right and Howard was one of two players unmarked to place his header past Kiraly.
As expected, the Eagles were more involved after the break and within seven minutes of the restart Johnson was on target from close range after Luton failed to clear Ben Watson's corner.
Teenage goalkeeper Dean Brill making a rare appearance in place of the injured Marlon Beresford, made a top-class diving stop to deny Johnson and then produced another splendid block from Jobi McAnuff.
Just as Palace were looking more threatening, Luton delivered the killer blow.
Nicholls' free-kick not far from the corner flag bobbled into the goalmouth, Palace reacted hesitantly and although Howard was on hand, Brkovic was first to the ball and rolled it over the line.
Palace offered little constructive after that and Luton coped with ease to earn a welcome three points.