Jennison Myrie-Williams and Febian Brandy grabbed the goals while goalkeeper Peter Gulacsi produced a crucial penalty save in a commanding display.
Hereford had a great chance to take the lead in the 20th minute when Myrie-Williams showed a lot of pace to get clear of two defenders and race into the Leeds area.
But the winger, on loan from Bristol City, lifted his shot over keeper Casper Ankergren and over the bar in his excitement.
Leeds spurned a glorious opportunity of their own to take the lead eight minutes from the interval.
Chris Taylor was judged to have brought down Andy Robinson and a penalty was awarded.
Lee Trundle struck his spot-kick firmly but Gulacsi dived to his right to turn the ball away for a corner.
Two minutes later Hereford were in front.
Sam Hewson slipped the ball through to Myrie-Williams whose left-foot shot, on the angle from 12 yards, flashed into the corner of the net.
Shortly after the start of the second period, only a fine challenge by another on-loan player, Liverpool centre-back Godwin Antwi, who had an excellent debut for the Bulls, prevented Luciano Becchio from drawing his side level.
But it was Hereford who continued to look the more dangerous side and they deservedly increased their lead on 63 minutes.
Myrie-Williams swung in a free kick from the right which Antwi headed across the goal for Brandy to flick home.
Hereford could have increased their lead through Steve Guinan, whose volley went just over.
And although Robinson and Becchio had chances for Leeds, the Yorkshiremen ended well-beaten on the night.