Second-from-bottom Torquay turned the form book upside down to take a sixth-minute lead through striker Elliot Benyon.
Benyon pounced from six yards out after Plymouth goalkeeper Luke McCormick made a brilliant one-handed diving save to keep out Damien Mozika's goal-bound 18-yard strike.
Plymouth took three minutes to level, striker Reuben Reid thrashing a ninth-minute spot-kick down the middle after Nathan Craig was judged to have blocked Luke Young's free-kick from the left with his hands.
Reid whistled a 20-yard volley just wide while at the other end Jordan Chapell beat three players before taking a return pass to send a 30-yard dipping shot towards goal, where McCormick just got enough hand to the strike to turn it on to the face of the bar in the 40th minute.
Torquay keeper Martin Rice made a superb 74th-minute save to keep out skipper Conor Hourihane's rising 20-yard free-kick, heading for the top corner. And from the resultant corner Argyle substitute Caolan Lavery's headed effort flew back off the upright.