Jaiden White took the lead for the away side in the 41st minute before an own goal from the Farsley keeper after an Omari Sterling-James free-kick made it two.
Andy Williams and Yusifu Ceesay then came off the bench to score the third and fourth respectively.
The win kept the Bulls in sixth whilst the Celt Army remained bottom.
Paul Caddis made one change to the side that beat Curzon Ashton last Saturday with debutant Kieran Coates replacing Aaron Skinner.
David Stockdale also made just one alteration to the team that lost to Spennymoor with Joao Silva returning to the side, after being away for international duty, in place of Dylan Youmbi.
Hereford had the first chance of the game in the seventh minute when Lawson D’Ath delivered a threatening cross into the box, he found Tate Campbell but he could not keep his header down.
The game quietened down after that with Caddis’ side dominating possession without creating anything of note.
That was until the 25th minute when Lewis Hudson found his way into the box, he fired towards goal from a tight angle but the ball flashed across the six-yard box and out.
The Bulls got the breakthrough in the 41st minute when White took a shot at goal which took a wicked deflection to send the keeper the wrong way to give the away side the lead, meaning it was 1-0 going into the break.
Hereford got the second 45 off to the perfect start when Sterling-James hit the bar from a free-kick, the ball then ricocheted off of the keeper and into the back of the net.
In the 65th minute, Sterling-James hit a spectacular effort from range which looked destined for the top corner if it was not for an equally brilliant save from Will Brook.
Farsley had their first chance of the game in the 76th minute when Dylan Youmbi picked out Tyler Polwarth inside the box who hit the post with a header.
Soon after Andy Williams made it three when Tate Campbell broke forward, he then found the substitute at the back post who tapped it home.
Ceesay then got in on the action when his effort from outside the area found its way past Brook and into the back of the net.
That was the final action of the game meaning it finished 4-0.
Hereford FC XI- T. Richardson, K. Coates, M. Preston (A. Skinner 63’), K. Howkins, L. Hudson, T. Campbell, L. D’Ath (D. Mitchell 79’), A. Babos (Y. Ceesay 63’), J. White (J. Cowley 74’), O. Sterling-James, R. Campbell (A. Williams 63’)
Farsley Celtic XI- W. Brook, I. Abankwah (L. Edmondson 87’), E. Janneh, T. Polwarth, C. Bumhira (D. Youmbi 69’), C. Hyde, C. Kondolo (E. Ameho 81’), M. Mampala, R. Monteiro, J. Iwobi (T. Priestley-Standing 81’), J. Silva
Unused Sub: H. Sheridan
Attendance: 305
