The Reds outplayed the Bulls for large periods of the game, but were punished for two slips at the back by Guy Ipoua and Tamika Mkandawire.
The visitors made the better start to the game and could have been 2-0 up with just two minutes gone, Jon Brady blasted over unmarked from the edge of the box after being set up by a neat volley from Ryan Green.
Adam Stansfield who scored in the 1-1 draw against Crawley last season, then fired straight at keeper Phil Smith from ten yards.
Having survived the early pressure, Crawley began to enjoy the majority of possession and almost took the lead on 33 minutes.
Simon Wormull latched on to a through ball by Jamie Cade and curled an effort with the outside of his right foot against the far post.
Hereford looked more dangerous after the break and took the lead on 58 minutes. Green was allowed to run unmarked down the right flank and his cross found an unmarked Ipoua, who sidefooted home from six yards.
Crawley went for broke in the final 25 minutes by bringing on striker Danny Davidson to play in a three-man attack alongside Steve Burton and Stuart Douglas.
The change initially made a difference with the Reds going close through an angled volley from Burton which flashed inches over and a low drive from Douglas that whistled just wide of the right-hand post.
However, Hereford sealed the points eight minutes from time when Mkandawire bundled the ball in from two yards after Smith had made a mess of a punched clearance from a corner by Alex Jeannin.
The visitors made the better start to the game and could have been 2-0 up with just two minutes gone, Jon Brady blasted over unmarked from the edge of the box after being set up by a neat volley from Ryan Green.
Adam Stansfield who scored in the 1-1 draw against Crawley last season, then fired straight at keeper Phil Smith from ten yards.
Having survived the early pressure, Crawley began to enjoy the majority of possession and almost took the lead on 33 minutes.
Simon Wormull latched on to a through ball by Jamie Cade and curled an effort with the outside of his right foot against the far post.
Hereford looked more dangerous after the break and took the lead on 58 minutes. Green was allowed to run unmarked down the right flank and his cross found an unmarked Ipoua, who sidefooted home from six yards.
Crawley went for broke in the final 25 minutes by bringing on striker Danny Davidson to play in a three-man attack alongside Steve Burton and Stuart Douglas.
The change initially made a difference with the Reds going close through an angled volley from Burton which flashed inches over and a low drive from Douglas that whistled just wide of the right-hand post.
However, Hereford sealed the points eight minutes from time when Mkandawire bundled the ball in from two yards after Smith had made a mess of a punched clearance from a corner by Alex Jeannin.