Thorpe followed up leading scorer Jamie Ward's third minute opener as Torquay breathed new life into their hopes of avoiding relegation and stretched the Mariners' nightmare run to seven straight defeats.
And Martin Paterson's 88th minute consolation effort was Town's first goal for 550 minutes.
Ward gave Torquay a flying start with his eleventh goal of the season, lashing home a right-foot volley after coolly controlling a deflected shot by Matt Hockley.
It was no more than the Gulls deserved as they ripped into their opponents from the first whistle.
Veteran on-loan goalkeeper Kevin Miller from Southampton and new left-back Mark Robinson from Stockport both bolstered Torquay's defence on their debuts.
But it was Thorpe, outstanding throughout, who was the star of the show, especially after Ward had to limp off with a knee injury after only 17 minutes.
In the 44th minute he latched on to Stephen Cooke's through-ball to score his first goal with a right-foot shot in off the post.
Paterson, easily Grimsby's best player on the night, hit the bar in the 57th minute, but there was no stopping Thorpe.
He grabbed his second from a rebound in the 58th minute after Cooke hit the post and then completed his hat-trick with an 82nd minute penalty after Nick Fenton had brought him down.
Paterson deserved his late goal, but it was far too little and too late for Grimsby.
The result cut the gap at the bottom of League Two to four points, as well as improving Torquay's goal difference considerably.
Grimsby, who have been dragged even deeper into trouble, had Fenton booked for the foul which conceded the penalty for Thorpe's hat-trick.
And not even the 73rd minute introduction of veteran striker Tony Thorpe, signed this week from Stevenage, could give the willing Paterson the support he needed.