Matt's winner came 20 minutes into the second half and followed a period of sustained pressure on the home goal.
Junior Brown set up the chance by threading a pass through from midfield, where the visitors' record signing turned Sonny Bradley and hit a low shot wide of goalkeeper John Sullivan.
Effective on the counter-attack, Fleetwood deserved their sixth win in eight matches.
They created the best chance of an entertaining first half when Matt rifled a shot against an upright - goalkeeper Sullivan deflecting the ball away for a corner.
The opening 45 minutes was an evenly contested affair, but as the game progressed Fleetwood gained the upper hand and seldom looked likely to lose their lead once Matt had netted.