Davon Marshall scored 16 and JR Coronado added 10 and a career-high 18 boards for Liberty (10-19).
Marshall moved into fourth place all-time in 3-point field goals made for Liberty.
After Coronado’s layup with 1:15 remaining pushed Liberty’s lead to 65-62, Travis Betran connected from behind the arc to tie the game at 65-all with 26 seconds left. Marshall’s missed 3-pointer with 2 seconds left sent the game into overtime.
Liberty scored the first six points of the extra period—Speaks made a jumper followed by layups from Marshall and Sanders—to go up 71-65 with 3:26 remaining.
Austin Peay (7-22) made it 71-69 on Chris Horton’s free throw, but the Flames made eight free throws in the final 1:28 to seal the victory.
Anthony Campbell scored 21 points for the Governors.