Substitute Yoann Arquin scored twice after Joe Colbeck's 54th-minute opener to leave Hereford needing to beat Torquay in their final game to stand a chance of staying up.
The Red Devils, meanwhile, remain in third place after Crewe's last-gasp equaliser against the Gulls. Colbeck broke the deadlock nine minutes after the break by sliding the ball in from close range after a mix-up involving keeper Michel Kuipers and Dean Howell following a through-ball from Delroy Facey.
Crawley came close to equalising when Sergio Torres rifled a poor clearance from keeper Adam Bartlett against the cross-bar. Keeper Bartlett superbly tipped over a 30-yard drive from Scott Davies before diving to save a goal-bound shot from Billy Clarke.
But Arquin doubled Hereford's lead on 77 minutes from point-blank range after Facey set him up by rounding Kuipers. Arquin struck again five minutes later by latching onto a long ball forward to beat Kuipers with a low left-footed strike.