Chris Horton added 20 points and 16 rebounds for Austin Peay (12-18, 6-10 Ohio Valley Conference), which made 21 of 25 free throws (84 percent).
UTM (8-23, 3-13) opened the game with an 11-0 run, but the Governors responded with a 13-2 spurt to tie the game at 13 with 11:24 left in the first half. The contest featured 12 ties and 19 lead changes.
Will Triggs' dunk with 4:16 remaining gave Austin Peay a seven-point lead - its biggest of the game - but a 10-2 run gave the Skyhawks an 81-80 advantage about 2 minutes later.
The Governor hit 8 of 8 free throws in the final 1:46 to seal the win.
Terence Smith led the Skyhawks with 20 points.