Lewis Alessandra chested in skipper Conor Hourihane's 85th-minute cross from the left for Plymouth's second goal which sealed all three points and local bragging rights.
On-loan Sheffield Wednesday striker Caolan Lavery had earlier fired Argyle ahead with a superbly-taken first-time strike on the hour.
He could have doubled his tally three minutes later after United goalkeeper Michael Poke saved Reuben Reid's goal-bound shot.
The ball fell invitingly to Lavery - on three goals in four starts - but his measured side-footed shot from 10 yards was cleared off the goal-line by on-loan Blackburn centre-back Anthony O'Connor.
In between, United's Jordan Chapell tested Argyle 'keeper Luke McCormick with his second 30-yard effort of the second half.
United striker Karl Hawley sent a scissor kick just wide after 68 minutes as Torquay's second Devon derby in four days swung from end to end.
In the first half, Poke palmed over Alessandra's 11th-minute dipping strike and soon after denied Reid when the striker raced through one-on-one.