Brake also scored on a 50-yard pass from RJ Nitti in the second quarter. CJ Williams added two touchdowns for the Bison and ran for 164 yards on 17 carries.
Brake's winning score happened with 13:08 left in the fourth quarter with the score tied at 35. The Bison then held the Keydets to a late fourth quarter field goal for the win.
Bucknell's Matt DelMauro scored two touchdowns in the first quarter for an early 14-0 Bison lead.
VMI's Al Cobb responded with three touchdown passes in the second quarter, including one to Matthew Nicholson with under a minute to go in the half, to tie the game 21-21. He had 308 yards passing overall.