The visitors moved into fourth spot in the League One table after a comfortable fourth away win of the season, while Pools stay second from bottom with only one win to their name this season.
The only goal of an untidy game at Victoria Park came after 14 minutes. Pools failed to defend a corner with any conviction and visiting midfielder Hope Akpan sent a dipping volley low past Pools goalkeeper Scott Flinders.
The Pools keeper made two vital first-half stops to keep his team in with a shout. First he got down low to deny Jon Forte from close range and then stood firm to keep out a goalbound close-range effort from Nicky Adams.
It was 55 minutes before Pools got a shot on target, right-back Neil Austin drilling a low free-kick at goal that Paul Jones saved and the Crawley goalkeeper then denied the same player when his low, long-range shot was curling towards the bottom corner.