The Gulls, relegated from League Two last season, were ahead after just six minutes when Tim Sills slammed the ball past Nikki Bull from 18 yards having seen a shot blocked moments earlier.
Sills came close to making it two shortly afterwards but his close-range header from Kevin Nicholson's free-kick was parried to safety by Bull.
It was all Torquay as Tony Bedeau forced another stop from Bull, before Danny Stevens did extend their advantage in first-half injury time, firing the ball into the top corner from 12 yards.
Lee Phillips and Chris Zebroski had both spurned chances before the latter made it three in the 56th minute, heading home a Nicholson cross from close in.
Rhys Day had Aldershot's best chance late on, but his header drifted wide.