A first-half strike from Danny Williams was enough to give Hereford all three points against promotion rivals Exeter.
The decisive moment came in the last minute of the first half. City goalkeeper James Bittner was shown red for the second game in a row when he was adjudged to have deliberately handled outside the box. Danny Williams took full advantage for Hereford when he curled home the resulting free-kick.
Exeter had earlier had the first shot of the game in the third minute when James Coppinger drilled the ball into the arms of the goalkeeper after he was superbly found by Sean Devine.
Steve Flack then went close for the Grecians when he flicked on Alex Jeannin's corner, but his header was blocked on the line.
Exeter were the better side in the opening stages. Dwane Lee shot wide with a long-range shot and Jeannin blasted over the top as Exeter pushed forward.
Santos Gaia found Flack with a great throughball, but Matt Baker scampered off his line to smother the ball as the striker prepared to pounce.
Hereford's first shot at goal came just after the half-hour mark when Rob Purdie struck the ball over the bar from the edge of the box.
After the break Exeter pushed forward and Jeannin twice went close with shots from a tight angle.
Williams went close to stretching the lead for Hereford with a shot from a tight angle which was well saved by substitute goalkeeper Martin Rice.
Purdie blew a golden opportunity to put the game beyond Exeter when he blazed wide from only six yards on the hour.
Devine went close late on for Exeter when his volley from 30 yards landed on the roof of the net and he then saw a close-range shot on the turn superbly saved by Baker.