Two goals from Alan Connell, one in each half, extended Hereford United's unbeaten home run to six matches.
But the injury-hit visitors have some cause to feel hard done-by after dominating much of the play without being able to find the right touch in front of goal.
Wrexham made three changes from their Boxing Day line-up at Rochdale and one of the returning players, Gareth Evans was in the action inside the first 30 seconds.
The young centre-back mis-kicked to let in Tim Sills but then quickly recovered his error to boot the ball clear.
With Hereford making the early running, a snap-shot from Connell almost caught out goalkeeper Mike Ingham, but his 25-yard effort clipped the bar on the way over.
After that, it was Wrexham who made most of the running in the next phase and the visitors should have taken the lead on 17 minutes when Matty Done ballooned the ball over from 12 yards after good work down the left by Chris Llewellyn.
A minute later, Llewellyn's shot dribbled just past an upright with Wayne Brown scrambling across his goal-line.
On 36 minutes, Brown made a fine save to deny Marc Williams but the Bulls immediately broke down field to take the lead.
Simon Travis made ground down the left and crossed for Connell whose first-time shot beat Ingham, although the goalkeeper got a hand to the ball on its way in.
Ingham had to be alert at the start of the second period, charging off his line to beat Stuart Fleetwood to a Connell throughball.
But then, as in the first period, it was Wrexham who went on to have the better of the play.
Kevin Smith's shot clipped the outside of the post on its way behind and Brown had to pull off a fine save to tip over a header from Lee McEvilly.
Llewellyn might have done better than blaze wide from the edge of the area when Trent McClenahan only partially cleared a Simon Spender cross.
Two minutes from the end, however, Wrexham paid the full penalty for their wastefulness.
Travis broke clear on the left and slipped the ball inside to Andy Williams, who laid a pass into the path of Connell and he made no mistake with a precise shot from 20 yards.