A dreadful error after seven minutes by goalkeeper Gavin Ward gifted the opening goal to Kevin McIntyre.
The visitors seldom threatened thereafter but held out until the 58th minute when Wrexham-born Darren Moss rose unchallenged to head in Marc Tierney’s centre.
A crowd of 7,065 saw Wrexham attempt to hit back with efforts from Phil Bolland and Drewe Broughton.
But Shrewsbury made it three after 68 minutes when Ward saved Dave Hibbert’s penalty only for James Constable, on a minute earlier as a sub, to follow up.
Chris Humphrey missed a golden chance for a fourth but by then Wrexham’s travelling supporters were resigned to defeat and almost certain non-league football next season.