With only their second triumph since Boxing Day, Shrewsbury also allayed any lingering relegation fears while in turn making their old rivals racing, if not mathematical, certainties for the drop.
Although the margin of victory slightly flattered the home side, there was no denying them a first win under Paul Simpson who took charge a month ago - and their first win of any description since a 2-0 success against visiting Morecambe way back on January 19.
With both teams struggling for form and confidence the first goal in this crucial local derby was always going to be vital - and Shrewsbury were in no position to look a gift horse in the mouth when they were handed the opener by some dreadful Wrexham defending on eight minutes when Kevin McIntyre opened the scoring.
Second-half goals by Wrexham-born Darren Moss and substitute James Constable ensured the points as Shrewsbury brought their long barren spell to an end.
In the seventh minute central defender Colin Murdock hoisted a free-kick downfield, and when ex-Shrewsbury centre-half Richard Hope and keeper Gavin Ward both hesitated they were punished to the hilt as McIntyre nipped in to head over the advancing Ward.
Once they settled, Wrexham pushed hard for a leveller and Marc Williams, Michael Proctor and Drewe Broughton all went close for the visitors, but their hopes of a comeback were dashed considerably when Moss headed home a Marc Tierney centre 13 minutes after the restart.
There was no shortage of spirit from the Welsh side, but any hopes of a dramatic revival were ended all together in the 68th minute.
Constable had only been on the field for a minute when he was sent crashing in the Wrexham penalty area by Phil Bolland.
Although Dave Hibbert saw his spot-kick saved by Ward, in the ensuing scramble Constable forced the ball home - netting his fourth goal of the season - to secure without doubt Shrewsbury 's much-needed victory.