Boro netted twice in the first half as they stay sixth in National North.
The Seadogs opened the scoring at Redditch through Rio Allan, inside 20 minutes.
Ste Walker doubled Boro's advantage, five minutes before half-time.
Hereford then added what turned out to be a consolation deep into added time.
Boro boss Jono Greening admitted to SAFC TV that the hosts caused a scare with that late goal:
" They did indeed. I think you know, we spoke to the boys before the game about what a big game it was for us trying to stay in the play-offs.
"What a big game it was for them because obviously they've got loads of games to play. They're in the relegation zone. They've got a new manager. Which is never easy. And they've got to start winning games to get out of the relegation zone. So we knew we had to start the game well, I thought we were very, very good.
"I think when we got the first goal, With Rio, from the corner, went straight in. That settled us down a little bit. And then, you know, you get the second goal. And I think half-time was just all about we talked about getting a clean sheet, which we didn't get, you know, due to the goal in the last minute.
"But I thought the second-half performance was good and professional. We did our job."
The result keeps Boro sixth ahead of Tuesday's trip to Alfreton.
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