Two first-half goals by substitute Ryan Lowe secured the Railwaymen their third victory of the season as the visitors' poor away form continued.
The result was never really in doubt once Lowe, a ninth minute substitute for the injured Lee Barnard, turned inside Alan Goodall before scoring with a fine finish for Crewe's second in the 39th minute.
Alex's first was set up by a surging run from on-loan youngster Simon Church. After Neil Cox had a shot deflected, Lowe had time to pick his spot at the near post with a fierce drive.
Luton barely threatened in the first half and with a bit more composure 18-year-old Church might have also got on the scoresheet but was denied by a six-yard box clearance by Jaroslaw Fojut and then a last-ditch tackle by Chris Perry after he had run half the length of the pitch.
But Crewe suffered more injury woes with Julien Baudet and George Abbey limping off and the changes seemed to upset their momentum. Luton were the better side in the second half but couldn't fashion any clear-cut chances.
Veteran striker Paul Furlong went close with a thundering header, one of several times he threatened the Crewe goal.
Lively right-winger David Bell went close and he glanced a Darren Currie header a yard wide. Crewe had a real let-off when, after Furlong flicked on with his head, substitute David Edwards cracked a first-time effort onto the foot of the post.
Matthew Spring also drove just over in the closing minutes but by and large Crewe were able to keep the Hatters at arms length as they closed out the game.