The Flames (7-2, 4-0 Big South Conference) scored three touchdowns on offense, two on special teams and one on defense.
The Keydets (2-7, 1-5) took a 7-0 lead on a 48-yard touchdown pass from Kyle Hughes to Mario Scott with 13:43 left in the first quarter.
Liberty tied the game 11 seconds later on Aaron Hewlett's 80-yard kickoff return, then took the lead on Bevins' 42-yard field goal. He also had kicks of 38, 40 and 43 yards.
Although VMI had 335 yards of offense to Liberty's 334, the Keydets committed eight turnovers, losing six fumbles.
Ian Childress scored on a 34-yard interception return for the Flames and Kevin Fogg recovered a fumbled punt return in the end zone.
Tim Maypray led VMI with 87 yards on 12 carries.