Substitute Ryan Lowe's first-half double guided Crewe to victory.
Luton striker Paul Furlong went close with a header before Lowe put Crewe ahead, just four minutes after coming on to replace the on-loan Lee Barnard.
Neil Cox's long-range effort ricocheted into the path of Lowe and the striker was able to fire a shot under the body of keeper Ben Alnwick on 13 minutes.
Lowe got his second five minutes before the break when he turned Alan Goodall before despatching a cool finish.
Crewe: Williams, Abbey (Roberts 51), Baudet (O'Donnell 45), McCready, Jones, Rix, Cox, Schumacher, Moore, Barnard (Lowe 9), Church.
Subs Not Used: Miller, O'Connor.
Goals: Lowe 14, 40.
Luton: Alnwick, Jackson (Robinson 70), Fojut, Perry, Goodall, Bell, Spring, Hutchison (Edwards 70), Currie, Andrew (Morgan 58), Furlong.
Subs Not Used: Coyne, Brkovic.
Ref: Eddie Ilderton (Tyne & Wear).