There was plenty of free-flowing action from both sides in the opening stages with Bradford City having the ball in the net after eight minutes, although Guylain Ndumbu-Nsungu's shot was ruled out due to a handball by Peter Thorne in the build-up.
But Hereford then took control with two goals in three minutes. On 15 minutes, Toumani Diagouraga raced on to Clint Easton's throughball and managed to escape the attentions of Paul Heckingbottom before driving his first Hereford goal past goalkeeper Donovan Ricketts.
The Jamaica international keeper was at fault with Hereford's second goal three minutes later.
Richard Rose drove in a cross from the left and Steve Guinan rose highest to head the ball through Ricketts' hands and into the net.
Ndumbu-Nsungu was unlucky in the 27th minute when he rifled a shot against the Hereford crossbar.
But fortunes changed a minute later when he was struck by a long-range effort from Eddie Johnson and the ball flew into the right-hand corner of Wayne Brown's net with the Bulls keeper heading the other way.
Hereford regained their two-goal lead just four minutes into the second period. Lionel Ainsworth showed lively pace to race on to a Ben Smith pass before being brought down by Heckingbottom.
Referee East pointed to the penalty spot and Trevor Benjamin rifled the kick past Ricketts.
But the Bantams were never out of the game and cut the deficit again on the hour-mark. Ndumbu-Nsungu held off the challenge of Bulls skipper Karl Broadhurst before drilling an angled drive past Brown.
The Bantams pressed strongly in search of an equaliser but were rocked in the 84th minute when Diagouraga raced clear to cross for substitute Theo Robinson to slip the ball past Ricketts to seal the points.