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."