The match never reached any great heights of entertainment in a tussle between two evenly-matched sides.
It was never pretty and Hereford worked hard without creating many clear openings. The closest they came to scoring was three minutes from the end when Tamika Mkandawire shot wide of an unguarded net.
They also nearly caught Wrexham out just before half-time when Alan Connell met a corner from Alex Jeannin with a header that Mike Ingham turned onto the crossbar before Ryan Valentine cleared with the Bulls claiming the ball had crossed the line.
Wrexham set the pace early on with Valentine having a long-range shot saved and Darren Ferguson providing a cross from which Danny Williams headed over the crossbar.
New striker John McAliskey thought he'd scored when he got up to meet a Ferguson corner and headed towards the net but Simon Travis cleared off the line at the back post.
Chris Llewellyn tried a 45-yard lob that caught Wayne Brown off his line but his effort went over the bar.
Brown had to be sharp in reacting to save a shot from Matty Done that took a deflection and nearly crept inside the post. Travis also headed off the line again from McAliskey's header following a Ferguson corner.
Hereford pushed up to create a couple of slight openings, Connell heading wide from Jeannin's free-kick and then shooting past the post after Stuart Fleetwood's initial shot had come back to him.