Matt applied the finishing touch to an inch perfect defence-splitting pass by experienced Town substitute Jon Parkin.
After a dour first half the game finally sparked into life when Torquay left back Kevin Nicholson sent Chris Maxwell diving at full stretch from a free kick.
Forward Elliot Benyon pounced on a slip by Alan Goodall to force the Fleetwood keeper to flap over his deflected chip from the right.
Recalled Gulls keeper Martin Rice made a superb save to deny Fleetwood striker Matt as the visitors countered and the striker broke into the penalty area from the right.
Rice made another vital save, getting just enough on Antoni Sarcevic's angled shot from the right to deflect it on to the foot of the far post and away to safety.
Central defender Aaron Downes received the biggest early cheer when he let fly with a dipping 40 yarder in the 21st minute to show his shot-shy Torquay team-mates the way to goal.
But it was the combination of Parkin and Matt that ultimately decided the contest with, fittingly, the best move of the game.