Graham Turner's men needed to better Wycombe's result against Southend but the Chairboys' 3-1 win left the Shrews facing a play-off date with Torquay.
Victory for Shrewsbury meant they won four and drew one of their last five games without conceding a goal but they came up just one point short of Wycombe.
Neither side conjured a direct shot on goal in the first half but things changed dramatically in the 52nd minute when big striker Matt Harrold was called up off the bench and created the vital breakthrough.
He showed deft control before stroking the ball out to midfielder Mark Wright who jinked his way around Damien Batt and fired home his 14th goal of the season.
Harrold crowned a match-changing performance in the 77th minute when his slide rule pass set up David Davis for the second and in the final minute provided an encore for sub Lionel Ainsworth to add the third.