The Governors (5-5) reclaimed a lead after Ed Dyson hit a 3-pointer to ignite a 10-0 run, making the score 54-45 midway through the second half.
Liberty (4-6) climbed back within two after a John-Caleb Sanders layup, but Austin Peay used another surge capped off by a Betran 3-pointer to take a 10-point lead with 3:30 remaining. Antwan Burris hit a 3-pointer and Sanders made a layup to cut the deficit to five, but with just four seconds left.
Austin Peay shot 52.1 percent from the field and had four starters score in double figures. Will Triggs scored 12 points and Dyson had 10. Demarius Smith finished with 12 assists and six boards.
Burris paced the Flames with a career-high 27 points and Sanders contributed 16.