Backed by a huge travelling support who had made the short journey up the A49, the visitors fell behind to an early Asa Hall goal, but were level through Simon Johnson just before the half-hour, before Gary Hooper settled the outcome with 23 minutes remaining.
But while Graham Turner would have enjoyed his return to the club for whom he played and managed with such distinction in the late seventies and early eighties, Shrewsbury remain anchored in mid-table, with little prospect of making a play-off place after their sixth game without a win and a seventh home defeat of the season.
The Shrews began brightly however and when Ben Herd's pass split the Hereford defence on six minutes, Hall was on hand to sweep Town into the lead.
In the blustery conditions both sides struggled to find any rhythm to their play and often this was a scrappy, untidy affair, but Hereford managed to draw level in the 27th minute when a strong run from Sherjill MacDonald caused havoc in the Shrewsbury penalty area.
Twice goalkeeper Glynn Garner came to his sides rescue during the ensuing goalmouth scramble, although eventually the ball fell to Johnson who rifled Hereford level with angled drive from eight yards.
After the break and with the strong wind in their favour, the visitors gained the upper hand. Garner had to be smart off his line to deny MacDonald, but Shrewsbury had no such reprieve in the 67th minute.
Gary Hooper pounced to nod home from close range, after MacDonald had headed a cross back into the goalmouth.
Shrewsbury pushed hard for a leveller, but Kevin McIntyre and Guy Madjo were unable to convert late opportunities to snatch a point.