Huddersfield Town won away under boss Lee Clark for the first time at the tenth attempt, thanks to Michael Collins' second-half strike.
But the result plunges the Bulls even further into relegation trouble at the foot of the League One table.
In a first half full of attacking football there were plenty of chances at both ends.
Hereford were the first to threaten when Jennison Myrie-Williams thundered in a drive, which was turned away for a corner by Alex Smithies.
The Terriers goalkeeper saved well again shortly afterwards from Febian Brandy.
But the traffic was far from one way and United keeper Peter Gulacsi pulled off a fine double save to deny Anthony Pilkington.
Gulacsi saved well again from the former Stockport man, but was then lucky to get away with a weak punch which Danny Cadamarteri lobbed back over the bar.
Steven Guinan and Brandy both went close as Hereford enjoyed a good spell just before the interval.
But the dangerous Pilkington came close to giving Town the lead just before the break with a flashing drive which went inches wide.
Hereford lost Dean Beckwith with a knee injury at the interval, but still threatened in the early stages of the second period.
Good work by Kris Taylor set up a shooting chance for Brandy, whose angled drive flashed across goal and wide.
But Huddersfield always posed a threat and Pilkington fired narrowly over before having another shot grasped by Gulacsi.
It was midfielder Collins, however, who grabbed the crucial goal, prodding in after Gary Roberts' cross had been flicked on.
After that, although Hereford substitute Andy Williams had a shot deflected into the side-netting, the Bulls rarely looked like opening up the Town defence as the relegation trap-door begins to creak ominously open.