Hot-shot striker Theo Robinson fired in his sixth goal in seven games as high-flying Hereford out-muscled the Bantams on a treacherous pitch.
The highly-rated youngster opened the visitors' account with a close range finish after just 18 minutes and although City gave their all they were never able to get back on level terms.
The game had been in doubt because of a pre-match downpour, but it was Hereford who enjoyed the luck of the bounce as the players struggled to deal with the tricky surface.
The Bantams were fuming after referee Graham Laws awarded a free-kick against Omar Daley and Robinson rubbed salt in the wound by firing in the opener.Simon Johnson's low free-kick skidded through the City defence and fell kindly for Robinson who shot home from eight yards to bag his 10th league goal of the campaign.
City responded well but Hereford keeper Wayne Brown did brilliantly to tip away Daley's curling shot soon after.
Mr Laws upset the home fans with a series of disputed decisions and their mood darkened when United centre-half Dean Beckwith headed home from Johnson's left-wing corner seven minutes before the break.
Two minutes before the interval Bantams' skipper David Wetherall threw them a lifeline when he reacted quickest to fire home from close range after Brown failed to hold a Joe Colbeck shot.
United always looked threatening from set pieces and in injury time they punished Bradford again when Trevor Benjamin lashed home a shot from 12 yards.
City striker Peter Thorne headed inches wide at the start of the second half, but only string of fine blocks by Bradford keeper Donovan Ricketts prevented a rout.
Robinson should have grabbed his second 15 minutes from time after a superb pass from Clint Easton, but the striker failed to find the net with only Ricketts to beat.