Hereford maintained their promotion push as Crawley plunged deeper into relegation danger thanks to Guy Ipoua's late winner.
The Cameroonian struck with three minutes to play but, until then, the visitors had looked good value for a point after Danny Brown's well-struck drive had equalised Andy Williams' early opener.
Hereford took the lead on seven minutes when the Crawley defence presented the ball to Williams on the edge of their own penalty area.
The 19-year-old neatly side-stepped goalkeeper Phil Smith and held off the challenge of Ben Judge before sliding the ball into an empty net.
Crawley should have equalised on 18 minutes when Steve Burton slipped a pass through to Chris Giles who dragged his effort across goal and wide with a clear sight of the target to aim at.
In a generally scrappy half, Hereford came closest to adding to their tally on 27 minutes when Rob Purdie raced into the Crawley area and fired a low drive into the side-netting.
Giles saw a header clip the crossbar as Crawley opened the second period with a flourish but their equaliser still came somewhat out of the blue.
The Hereford midfield gifted the ball to Brown 30 yards out and his first-time shot flashed into the net before the home defence had moved.
Long-range efforts from both sides were all that could be mustered for some while after that and the game seemed to be heading for a draw before a moment of quality from Ipoua.
The experienced striker found space to leap and direct his header from Danny Carey-Bertram's cross over Smith and into the net to give Hereford three important points.