The Governors (6-13, 3-3 Ohio Valley Conference) have won three in a row for the second time this season.
The Tigers (10-10, 3-4), paced by Robert Covington, who matched his career high with 30 points and also grabbed 15 rebounds, led most of the first half. Tennessee State had its largest cushion at 13-4 and held a 29-28 advantage at halftime.
There were eight ties and nine lead changes after the break. With 2:54 remaining and the score knotted at 59, Fraley scored four straight points to spark an 8-0 run and a 67-59 Austin Peay lead with 25 seconds to go.
Although the Governors were only 2 of 6 from the free-throw line down the stretch, Tennessee State countered with just two baskets.