The first effort of the match came in the fourth minute, when a corner kick fell to Liam Kelly just outside the Fleetwood box, but the Latics captain fired over the bar.
The home side came close again just before the quarter-hour mark, with Forte picking up the ball from a counter-attack before blasting an effort just wide.
Oldham kept pushing forward, troubling the Cod Army defence time and time again, but Danny Philliskirk, Carl Winchester and Dominic Poleon all passed up chances before the deadlock was broken in first-half injury time.
Philliskirk was felled in the Fleetwood box, which prompted the referee to give the home side a penalty. Forte made no mistake from the spot to put Oldham a goal up just before the break.
The second half started slowly, with neither side troubling the opposition goal until just after the hour mark, when Poleon, collecting a pass from Philliskirk, forced a good save out of Scott Davies.
With Graham Alexander's side unable to conjure up a response, the game ended with Oldham gaining all three points which see them climb to 11th place in the table.