Jaiden White took the lead in the 56th minute before Remaye Campbell made it two 11 minutes later.
Michael Afuye pulled one back late on before Yusifu Ceesay wrapped up the three points in the final moments.
The win moved the Bulls back into the play-offs in sixth whilst the Nash dropped out and down to eighth.
Paul Caddis made four changes to the side that lost to Scarborough with Kyle Howkins, Tate Campbell, Lawson D’Ath and debutant Omari Sterling-James replaced by Levi Andoh, Dylan Mitchell, Declan McGlynn and Ceesay.
Craig Mahon made three alterations to the team that drew to Radcliffe with himself, Jimmy Spencer and Luke Griffiths dropped for Matthew Litherland, Alex Curran and Luke Griffiths.
The away side had the first chance of the game in the seventh minute when Stefan Mols received the ball on the right wing, he drove into the box and curled a shot at goal but it was well saved by Theo Richardson.
Other than that chance the game got off to a quiet start with both sides cancelling each other out.
Curzon Ashton had an opportunity on the counter in the 20th minute when Curran picked up the ball on the right, he took it forward and cut inside onto his left foot but his effort was just over.
Mahon’s side kept up the pressure soon after when a corner was taken short to Litherland who picked out Mols inside the box but his header hit the side netting.
After a quiet period, the Bulls had a great opportunity just before half-time when Tate Campbell picked out Remaye Campbell at the back post but his header skimmed the post and went out for a goal-kick.
Caddis’ side kept up the pressure a few minutes later when Tate Campbell rattled the bar with a fantastic effort on the volley, the ball then came back out to Sterling-James who found Remaye Campbell but his header was straight at the keeper.
That was the final action of the first half meaning it was 0-0 going into the break.
Hereford got their reward in the 56th minute when the ball dropped to White on the edge of the box following a long throw, he then hit an excellent volley past Jones and into the bottom right corner.
Remaye Campbell made it two in the 67th minute when the visitors gave the ball away trying to play out from the back, it then fell to the striker who put it past the keeper from close range.
The visitors pulled one back in the 82nd minute when Will Hayhurst delivered a cross into the box which found Michael Afuye who headed the ball across goal and past Richardson.
Ceesay secured the 3-1 win in the 92nd minute when he latched onto a long ball in behind, he then hit a delightful chip over Jones and into the back of the net.
Player/manager Mahon was then sent off shortly after for what appeared to be dissent.
Hereford FC XI- T. Richardson, A. Skinner, M. Preston, K. Howkins, L. Hudson, T. Campbell, L. D’Ath, A. Babos (Y. Ceesay 76’), O. Sterling-James (D. Sturridge 90+4’), J. White (D. Mitchell 87’), R. Campbell (A. Williams 90+4’)
Unused Sub: J. Cowley
Curzon Ashton XI- B. Jones, T. Sobowale, M. Poscha, L. Lacey (L. Griffiths 61’), I. Buckley-Ricketts (M. Afuye 70’), I. Sinclair, A. Curran (C. Mahon 81’), S. Mols (M. Kouam 61’), W. Hayhurst, M. Litherland, A. Barton
Unused Sub: J. Ollerenshaw
Attendance: 2642 (30 away)
