Fraley added nine rebounds for the Governors (14-8, 8-2 Ohio Valley Conference), who outscored the Colonels 7-2 in the final 3:14 after they had cut Austin Peay's lead to 54-50.
Terry hit two free throws and a layup for a 58-50 lead with 2:56 remaining, before Eastern Kentucky's Spender Perrin's layup cut the deficit to 58-52 with 2:36 to play.
It was the last basket for the Colonels, who missed their final three field-goal attempts.
There were eight ties and nine lead changes in the game.
Caleb Brown added 11 points for Austin Peay, which outrebounded the Colonels 37-24.
Perrin led Eastern Kentucky (11-10, 5-5), which had won four straight, with 19 points and 10 rebounds. Justin Stommes added 18 points.