Jonathan Douglas headed the only goal of the game just before the hour, glancing Alan Judge's left-wing cross past the despairing hand of goalkeeper Paul Jones.
And with Rotherham losing at Sheffield United, the Londoners stretched their points advantage to nine over the Millers.
It was one-way traffic as the Bees laid siege to the visitors' goal against a resolute and well disciplined Crawley defence.
Clayton Donaldson could have put the hosts ahead inside three minutes, flashing a low drive across goal.
Judge volleyed inches wide and Alan McCormack stung the keeper's hands with a fizzing low drive as Brentford piled forward trying to break the deadlock.
After Douglas opened the scoring, Stuart Dallas almost made it two with a blistering drive brilliantly saved by the legs of keeper Jones.
Dallas might have eased the Griffin Park crowd's nerves in the dying minutes, which also saw Paul Connolly clash with a home supporter, but his low sidefooted drive from a Jake Bidwell cross was blocked on the line.