The game began frantically, with the Gulls winning three corners in the first three minutes and Karl Hawley being denied at point-blank range by goalkeeper Sam Slocombe.
Just three minutes later, Eddie Nolan was dispossessed and then beaten on the far side, with Courtney Cameron's cross coming off the underside of the bar.
The deadlock was broken when Matthew Sparrow was felled in the Torquay box, prompting the referee to give the away side a penalty. Sam Winnall slotted the ball into the bottom right corner to gift his side the lead.
The beleaguered home side could have pulled it back when they won a penalty of their own at the end of the first half, but Dale Tonge's effort was saved by Slocombe.