Matthews finished with 143 receiving yards on five first-half catches for the Commodores (9-4), who blew a 24-0 halftime lead but then scored the game's final 17 points.
Patton Robinette completed 6-of-19 passes for 154 yards with two TDs and two interceptions and carried 15 times for 37 yards with a score.
Jerron Seymour and Brian Kimbrow combined for 164 rushing yards and two scores for the Commodores, who ended with consecutive nine-win seasons for the first time in school history.
John O'Korn went 20-of-47 through the air for 228 yards, two scores and two pick-offs for the Cougars (8-5).
Markeith Ambles made six grabs for 105 yards with a TD. Deontay Greenberry finished with six catches for 96 yards and a touchdown.