Tre Mitford’s second-half header secured the points as the Saints enjoyed their return to St James Park after three successive away games.
There was little to write home about during an even first half but Brackley dominated after the break and took the lead on 53 minutes when a fine run and cross by Matt Lowe set up a goalmouth scramble, which was eventually finished by Mitford.
Twariq Yusuf fired over after another break-away by Lowe, who also had an effort cleared off the line, while only a fingertip stop from Brandon Hall denied Mitford a second.
The closest Hereford came was a double chance as first Jaanai Gordon and then Tom Owen-Evans were denied by Danny Lewis.
Krystian Pearce received a straight red card for a challenge on substitute Wes York late on and it was York’s fierce effort that was close to doubling Saints’ lead and sealing the win in added time.
“It was an important win after losing as we did at Kettering last Sunday so it is a pleasing response to that,” manager Wilkin said.
“Hereford kept asking questions of us but once we re-grouped at half-time there was a period where we were very good, we scored the goal and had some really good moments.
“Their goalkeeper pulled off a wonderful save to deny Tre a second goal and keep it interesting going into the final period.
Hereford did well and kept us fighting all the way to the line.
“ It was enjoyable to be back here on home territory with the good support we’ve got and to be rewarded with the result.”
Brackley will now have the chance to move seven points clear at the summit when they seek to avenge that loss at Kettering in the return all-Northamptonshire fixture at St James Park on Tuesday night.