Only 13 minutes of this often scrappy, untidy encounter, remained when second-half substitute Derek Asamoah held his nerve to fire home from nine yards.
It was tough luck on Torquay who had gone closest to scoring until the goal when a first-half long-range effort from Dean Gordon had struck the Shrewsbury crossbar.
But another defeat leaves them anchored to the foot of the table with their Football League days seemingly numbered.
Shrewsbury made a bright start, befitting a team defending a 12-match unbeaten league run, stretching back to Boxing Day. Twice in the opening ten minutes striker Andy Cooke went close with headers, but it was in the 13th minute that the first-half deadlock was very nearly broken.
After a Torquay raid had been cleared, Gordon let fly from fully 45 yards only to see his dipping shot strike the woodwork.
As the half unfolded Shrewsbury's forward play lost its way and it was only with the introduction of the speedy Asamoah at the start of the second half that they once more began to carry a threat.
Ten minutes after the break he was denied at close range within seconds by Simon Rayner, the Torquay goalkeeper, saving an initial effort with his feet before diving to push away Asamoah's follow up.
There was little seen of Torquay as an attacking force in the second half and, with Shrewsbury holding the upper hand, Asamoah and Wales Under-21 midfielder Dave Edwards - who was released from the full Welsh squad on Friday to return to Gay Meadow - both went close before the visitors' resistance was finally broken.
Centre-back Kelvin Langmead headed a Marc Tierney free-kick across the goalmouth, and when the Torquay defence was unable to clear, Asamoah was on hand to fire home his eighth goal of the campaign.