Bulls blunders prove costly.
Morecambe cashed in on two of them through Danny Carlton and Phil Jevons before half-time and midway through the second period Stewart Drummond wrapped up the points.
The visitors were quickly into their stride and Adam Bartlett did well to tip Carlton's 20-yard drive over the bar. Harry Pell then turned a Jevons cross onto the post and away for a corner.
The Bulls gradually got into the game and began to put together some good moves without applying the finishing touch. But just when Hereford looked in control Carlton opened the scoring in the 32nd minute. Bartlett looked to have his 20-yard drive covered but the ball spilled out of his hands into the net.
On the stroke of half-time Michael Townsend gave away a free-kick just outside the home area and Jevons found a way through the wall.
At the start of the second period Hereford forced four quick corners while Barry Roche did well to turn Ryan Green's header away for a corner.
In the 57th minute, however, the Bulls failed to clear a corner and Drummond rifled in a volley, a lead the visitors protected.