Lauri Dalla Valle's brace helped Crewe overcome out-of-form Crawley, who are without a win in six matches.
Mark Connolly and Gary Alexander failed to add the finishing touches to Nicky Adams's pinpoint deliveries as the Red Devils bossed the early stages.
But Alex gained a foothold in the game when Dalla Valle, on loan from Fulham, headed in Luke Murphy's free-kick.
And the Finnish striker rounded off the win when he tapped home from Byron Moore's accurate centre.
VIEW FROM THE DRESSING ROOM
Crawley Town manager Richie Barker told BBC Sussex:
"The troubles they caused us in the first half or any other troubles came from mistakes of our own.
"But I thought in the first half we were excellent.
"We are creating the opportunities and we're just looking for someone to be a bit more ruthless.
"Unfortunately it's not there for us but the harder you work the luckier you get and we will continue to keep working harder."
Crewe Alexandra 13 Martin 02 Tootle 03 Davis 05 Ellis 15 Robertson 08 Murphy 19 Osman 26 Aneke 09 Pogba 11 Moore 30 Dalla Valle Substitutes 01 Phillips 06 Dugdale 12 Turton 16 Guthrie 31 Inman 07 M Clayton 27 Colclough Crawley Town 01 Jones 03 Sadler 04 Connolly 05 McFadzean (Walsh - 39' ) 19 Byrne (Ajose - 67' ) 06 Akpan 07 Clarke Booked 11 Simpson 16 Adams 21 Jones (Clifford - 84' ) 09 Alexander Substitutes 25 Kuipers 12 Walsh 13 Hunt 08 Torres 10 Clifford 15 Bulman 14 Ajose