Markus Heikkinen and Rowan Vine hit the goals in the first half, but dominant Town wasted a host of further chances to add to the score against a disorganised Eagles outfit.
Luton started off at breakneck speed and Tom Soares had to be alert in the third minute to clear Chris Coyne's header off the line from Dean Morgan's corner.
Eight minutes later another corner routine led to Town opening the scoring as Steve Robinson played a short flag-kick to Morgan, who crossed for Heikkinen to head home his first Luton goal from eight yards.
Palace almost hit back immediately as Dougie Freedman struck the post and from Jobi McAnuff's follow up, Kevin Foley nodded off the line.
But Luton continued to be first to every loose ball and they doubled their advantage in the 21st minute through a superb Vine finish.
Enoch Showunmi did well to work the opening for his strike partner on the edge of the area, but Vine did the rest as he blasted high into the net from a tight angle ten yards out for his third goal in five days.
Town continued to press and Peter Holmes almost scored in cheeky style as his attempted back heel from Carlos Edwards' cross went wide in the 33rd minute.
Three minutes later Luton again exploited the Eagles' weakness in the air as Coyne crashed a header against the top of the bar from Paul Underwood's free-kick.
Then on the stroke of half-time, Holmes should have made it three when as he struck Edwards' pull-back towards goal only for Boyce to get his body in the way.
The half ended with some unnecessary argy-bargy as Soares, Robinson and Holmes all saw themselves enter the referee's notebook after two ugly confrontations between both sets of players.
The second period continued in the same vein apart from a 50th minute run and shot from Michael Hughes.
Coyne, Edwards and Vine all went close to adding to the scoreline before Robinson saw a ferocious volley tipped over by Gabor Kiraly in the 74th minute.
Holmes then worked Kiraly again in the final minute with a well struck 20-yard volley.
Palace ended with four strikers on the field, but in truth they never looked like scoring.