Vale's winner came after 28 minutes when skipper Doug Loft's drive from the right channel deflected into the back of the net off striker Calvin Andrew.
The touch was enough to take the ball out of the reach of diving United keeper Michael Poke and into the far corner.
The goal came against the run of play and after Torquay central defender Aaron Downes had hobbled off with a hamstring injury.
Andrew's goal and Downes' injury were a double blow to new Torquay interim manager Alan Knill, whose sole change to United's starting 11 was to give on-loan striker Elliot Benyon his first start since rejoining United from Southend.
Vale keeper Chris Neal made a brilliant fifth-minute full stretch save to tip Rene Howe's powerful, downward header around the post.
Neal was again called into action to flap over Craig Easton's first-half free-kick following a foul on forward Ryan Jarvis.
Poke twice saved well from Ashley Vincent in the 70th and 72nd minutes as the visitors countered at pace, but Vale were forced to settle for their one-goal advantage.