Goals by Adam Stansfield and Andy Williams put Hereford in control at the break and Williams put the issue beyond doubt five minutes into the second period.
The first half was a scrappy affair lifted by three moments of high quality. The first of these came from former Hereford midfielder Jon Brady, making his first return to Edgar Street in U's colours.
The Australian was unlucky not to mark his visit with a goal when his spectacular 10th minute strike from 20 yards came back off the bar.
The next quality moment arrived on 33 minutes and it was Hereford who produced it. Striker Stansfield picked the ball up in midfield and raced past two defenders before planting an unstoppable angled drive from 20 yards past keeper Scott Howie.
Nine minutes later Williams got in on the act with a fine strike on the turn on the edge of the box which gave Howie no chance as it flew in off the bar.
The two strikers combined to make it 3-0 after just five minutes of the second half. Stansfield raced away down the right and delivered a perfect cross for Williams to sidefoot home.
The Bulls continued to dominate and the only surprise of the remainder of the game was that they failed to extend their lead.
Their best chance came on 71 minutes when new signing Stuart Fleetwood worked an opening for fellow newcomer Nicky Nicolau, who saw his right-foot shot come back off the post.