David Graham's sixth goal in six league games clinched a deserved victory and stretched in form Torquay's unbeaten run to six games.
The former Rangers starlet finished a jinking run with a 20-yard left-foot shot into the left-hand corner in the 77th minute.
It was no more than Torquay deserved, for they moved in to overdrive after Shrewsbury equalised early in the second half and briefly threatened to take over.
Torquay dominated the first half, taking the lead in the 18th minute through Jason Fowler. He cut in from the left wing and beat two defenders before curling a 20-yard shot in to the far corner.
Shrewsbury had only one effort at goal in the first half, Ian Stevens shooting just wide in the 35th minute, while Torquay went close through Graham, Matt Hockley and Graham again just before the break.
Torquay were down to ten men as Fowler was receiving treatment behind the goal, when Shrewsbury levelled in the 53rd minute.
Skipper Nigel Jemson stabbed in at the second attempt after Torquay failed to clear a Ryan Lowe corner.
Stevens volleyed a great chance wide for Shrewsbury in the 66th minute but after that it was nearly all Torquay, as Tony Bedeau set Graham up for his winning goal.
And in the last dozen minutes only Shrewsbury keeper Ian Dunbavin kept his side in the game, saving from Graham, Bedeau and substitute Neil Prince.
Torquay boss Leroy Rosenior said: "We knew Shrewsbury would get ten men behind the ball and, even though the final ball just let us down at times, we kept on and kept on probing and picking holes in them until we got through.
"And even when the crowd got frustrated in the second half we kept on passing."
"Graham has been getting the plaudits, and rightly so, but Martin Gritton worked his socks off and he's creating so much space for David up front."
Shrews manager Kevin Ratcliffe said: "We didn't work hard enough to stop them in the first half. We did in the second and I thought we were the better side until Torquay scored their second goal.
"Torquay are winning games and they are full of confidence, you could tell that."