The Hatters dominated the majority of the game and increased their unbeaten run to four games.
Matthew Spring grabbed an early goal before Crewe managed to score to make it 1-1 when Nicky Maynard was given space in the area, but the Hatters pulled in front again when Spring scored a penalty.
Luton make two changes to this afternoons team.
Ed Asafu-Adjaye goes straight into the starting eleven, making his first team debut, while Sol Davis replaces David Bell who went on loan to Leicester earlier this week.
Luton made an impressive start to the game with an early goal in the fourth minute.
Confusion between defender Danny Woodards and keeper Ben Williams saw the ball fall into the path of Spring who shot from 35 yards, past the keeper who had come of his line, and into an empty goal.
The visitors tried to get back into the game on ten minutes, when after an impressive run from Joe Anyinsah, Steve Jones was crossed the ball but found his shot at goal blocked by Don Hutchison.
The Hatters continued to dominate the game and had the chance to double their lead in the 19th minute when Paul McVeigh tried his luck from distance.
Stephen O'Leary was next to have a shot on goal from outside the area and was unlucky to see his attempt trickle wide of the post.
McVeigh got another chance on 36 minutes when he managed to find space through the defenders but again saw his shot go wide.
Spring almost made it a brace in the 42nd minute when another attempt from distance was heading goal bound, forcing the keeper to push the ball wide.
HALF TIME: LUTON 1-0 CREWE
The second half started in complete contrast from the first, with Crewe dominating the game and looking dangerous on the attack.
And Crewe's determination paid of when they found themselves on the score sheet on the 59th minute after a mistake from Keith Keane gave Maynard a clear passage into the penalty area.
Brill came out to try and prevent Crewe from scoring but unfortunately for the Hatters Maynard simply slotted the ball past him and into the net.
Luton had the perfect opportunity to get back in the lead when O'Leary set up substitute Calvin Andrew inside the area.
Despite only being 8 yards out, Andrew failed to get the ball past the keepers hands.
However, on the 77th minute, a foul on Ryan Charles inside the area gave the Hatters a penalty.
Spring stepped up to the spot and shot the ball under the diving keeper, putting Luton back in the lead.
With just a minute to go Spring almost made it a hat-trick when, after failing to find any space in the area Sam Parkin passed the ball back out of the area to the waiting midfielder.
But Spring found his shot pushed over the cross bar.
Luton: Brill, Hutchison, Parkin, O'Leary, Emanuel, Keane, Spring, Davis, McVeigh (Andrew 66), Charles, Asafu-Adjaye
Substitutes: Goodall, Currie, Robinson, Beavan
Bookings: Spring (72)
Crewe Alexandra: Williams, Woodards (McCready 72), Roberts, Baudet, O'Connor, Maynard, Abbey, Boyle, Lunt, Anyinsah (Moore 85), Jones (Bopp85)
Substitutes: Schumacher, Fon Williams
Bookings: Woodwards (47), O'Connor (54)
Referee: Mr Michael Oliver
Attendance: 5,465 (307 from Crewe)
