Exeter took an early lead through Lee Phillips but the Bulls took control with strikes from Guy Ipoua and former Grecian Alex Jeannin, before Ipoua was controversially sent off just before half-time.
The hosts made the best possible start when they went ahead in the fifth minute. A long ball from Dan Woodards picked out Phillips and the striker scampered into the box before firing a low shot into the bottom corner past Wayne Brown.
Against the run of play Hereford pulled level on the half-hour mark. Ipoua was found on the edge of the box and the striker twisted and turned before unleashing an unstoppable shot into the top corner.
The Bulls almost took the lead when City keeper Paul Jones made a hash of clearing a back pass and Ipoua fired a foot wide with a powerful shot.
Three minutes before the interval Hereford were ahead when Jeannin struck a free-kick into the top corner from the edge of the box.
While his team-mates celebrated the referee inexplicably flashed a red card at Ipoua, apparently for making obscene gestures to the crowd.
After the break Hereford continued to look dangerous. Andy Williams launched a powerful run and when the ball was knocked through to Adam Stansfield the striker fired just past the post from the tightest of angles.
Stansfield had another shot saved by the feet of the goalkeeper and Jones pulled off a double save from Danny Carey-Bertram.
Woodards headed just wide for Exeter in the dying minutes but the Bulls held on to secure an important victory.