Goals from Gary Hooper and Theo Robinson sent the Red Dragons down into the Blue Square Premier for the first time.
But the victory also improves Hereford's hold on the third automatic promotion place and opens up a four-point gap between the Bulls and chasing Stockport and Rochdale.
There was plenty of excitement in the opening exchanges with chances at both ends.
Matt Done forced an excellent save from Wayne Brown in the Hereford goal, with the ball being put behind for a corner, but Robinson missed a great chance to open the scoring with only four minutes played, blazing wide after being sent through by Hooper.
It was Brown who came to Hereford's rescue again on 33 minutes.
A long free-kick from goalkeeper Gavin Ward was flicked on by Mark Williams to Neil Roberts, whose fierce first-time effort was pushed behind for a corner by the United keeper.
Three minutes before the interval, the Bulls took the lead with a well-worked goal.
Sammy Igoe's pass was back-heeled by Robinson to Hooper, who raced on before driving home an angled shot past Gavin Ward.
Hereford made a bright start to the second period and Robinson raced away to fire against the foot of a post on 54 minutes.
Brown then saved well from Mark Williams before the Bulls extended their lead on the hour mark.
Richard Rose's cross from the left was flicked on by Hooper and neatly controlled by Robinson, who then struck his 11th league goal of the season, matching Hooper's total, under Ward.
Hereford continued to have their moments in attack, but were grateful again in injury time for the agility of Brown, who pulled off a superb flying save to deny Michael Proctor.