Daniel Carey-Bertram put the Bulls ahead after 36 minutes, firing home right-footed after being found by Danny Williams on the left.
The same player almost made it 2-0 after 70 minutes but was denied by a fine save from keeper Scott Tynan.
Joe Anyinsah also tested the home defence on several occasions as Hereford pushed on.
But Barnet were eventually beaten again by a 90th minute goal that sealed the points for the visitors - and it was a well-worked effort.
A fine pass from Craig Stanley from inside the Hereford half found Adam Stansfield, who twisted to fire a fierce shot into the net from inside the penalty area.
It was a well-deserved victory for Hereford who created the better chances as Barnet had an off-day.
The Bees started brightly enough, winning a string of early corners, but couldn't find a way into the match.