A brace from James Collins moved Shrewsbury up to second place in League Two as Torquay lost an away league match for the first time this season.
Collins scored his first when he finished well from 12 yards, converting from Lionel Ainsworth's low cross.
Torquay's Billy Bodin was denied by Ben Smith before Collins, who also hit the bar, grabbed his second when he pounced on Bobby Olejnik's poor clearance.
The Gulls ended with 10 men as Rene Howe was shown a second yellow card.
VIEWS FROM THE DRESSING ROOM
Torquay United manager Martin Ling tells BBC Radio Devon:
"In the first half we passed it well without effect, in the second half I thought it was a poor performance all round from all 14 players.
"As a team and a coaching staff we didn't do our job properly and right.
"The side that gets the first goal will win an awful lot more games, and we haven't done that on enough occasions."