The Shropshire side put in a workmanlike performance, settling the points with a header from Stewart Drummond just seconds before half-time.
Hereford had slightly better of the first period although they were rarely able to threaten the Town goal.
The visitors, whose direct style occasionally punched holes in the Hereford defence, also struggled to break through, but forced the first real save of the game on 38 minutes when a deflected shot from Derek Asamoah was grasped by the diving Wayne Brown.
On the stroke of half-time, Brown was in the action again flying through the air to claw an Andy Cooke shot for a corner. But from Ben Davies' flag-kick, Drummond was left unmarked to power a header into the corner of the net.
United should have levelled the scores from their best chance of the match ten minutes into the second period. An attempted shot by Simon Travis fell to the unmarked Tim Sills on the edge of the penalty area, but the former Aldershot man, who has scored just twice this season, fired high over the bar.
After that, it was the Shrewsbury attack which looked more dangerous with Cooke forcing a good save from Brown with a near-post header and then directing the ball just wide from another similar chance.
But Hereford almost snatched a point near the end of the game when substitute Alan Connell won a free-kick 25 yards out. The former Torquay man took the kick himself, but his shot deflected off the wall and went inches wide of the target.