Danny Carey-Bertram fired the home side ahead but Juan Ugarte had the Robins back on level terms within seconds.
Chris Llewellyn then ensured a final appearance for Denis Smith's cash-strapped side by striking 15 minutes from time.
Hereford should have been in front on 16 minutes when Adam Stansfield raced on to a Craig Stanley cross and produced an excellent cross from the left.
Rob Purdie was unmarked eight yards from goal as the ball came across but somehow misjudged the flight of the ball and missed his header altogether.
Four minutes later, another Stansfield cross produced a better result when Carey-Bertram was waiting to fire into the roof of the net from six yards out.
But the Robins were level within seconds when the sleeping Hereford defence left Ugarte unmarked and the Spaniard headed home his ninth goal in five matches.
As half-time approached Mawson saved twice to keep Hereford level, one a brilliant effort from Jim Whitley's swerving 25-yarder followed by a close-range parry from Ugarte.
Hereford began the second period in promising style with Stansfield's cross causing problems for the home defence.
But Llewellyn missed a great chance to net for the visitors, heading over a gaping goal before seixing on to a long throw from Andy Holt to blast in the decisive goal.
A late save by Ben Foster from Craig Stanley's drive preserved the win.