Clint Easton curled in an early free kick and then the visitors defended in depth, with Brown the hero as Mansfield's home hoodoo - one draw and nine defeats in 10 matches - continued.
Brown saved the best until last after beating away a 90th minute Mick Boulding penalty after Ben Smith had pulled down the 20-goal striker.
Then three minutes into injury-time, he clawed substitute Jefferson Louis' close-range finish away.
It was rough justice on the home side, who were led for the first time by caretaker-manager Paul Holland after Saturday's departure of veteran boss Billy Dearden.
Mansfield's early optimism was knocked back in the eighth minute from a disputed free-kick.
Easton took a long run-up and curled a 25-yard shot around the wall and into the bottom corner of the net.
The Stags though did not let the goal deflate them as first Matt Hamshaw's shot was turned around the post for a corner by the diving Brown and then from the flag-kick Nathan Arnold's 30 yard piledriver drew an even better finger-tip save from the keeper.
Hereford's neat, slick passing gradually penned the home side back and, from a Toumani Diagouraga cross, Alex John-Baptiste had to clear off the line.
The Stags were dealt a blow when experienced keeper Carl Muggleton limped off after suffering a groin strain nine minutes before half-time, but they fought back to dominate and create the better chances.
The Stags continued to surge forward after the break when they were playing into the teeth of a strong wind.
Mick Boulding was brought down by Dean Beckwith when clean through, but the Hereford defender was only yellow carded and the striker's free-kick hit the defensive wall.
Five minutes from time a spectacular diving save by Brown kept out Stephen Dawson's low drive at the foot of the post.
But the keeper kept his best save until last as the Bulls held on to boost their chances of automatic promotion.