Wilson scored on a 1-yard run in the third quarter as the Catamounts (1-5, 1-3 Southern Conference) pulled to within 10-7, then scored the game-winner early in the fourth on a 5-yard run.
The Bulldogs (2-4, 0-3) missed two field goals in the second half and turned the ball over on downs twice in the fourth quarter.
After Wilson's second score gave the Catamounts a 14-10 lead, the Bulldogs turned the ball over at the Catamounts 36.
On the Bulldogs' next possession, Bart Blanchard's pass fell incomplete on fourth-and-3 from the Catamounts' 15-yard-line with two seconds remaining.
Blanchard went 9-for-11 for 94 yards for the Bulldogs, including a 3-yard touchdown pass to Andre Roberts in the second quarter.