Austin Peay (6-11, 1-2 Ohio Valley) came from 11 points down and trimmed it to two on Damarius Smith's dunk with 26 seconds left. TSU's Xavier Richards missed a pair from the line, then fouled Josh Robinson, where he made the first of two free throws. Williams grabbed the miss of the second and converted to put Austin Peay up by one.
Khalil Davis pulled down Darrion Reddick's last-second miss to seal the Governors' win.
Tennessee State (3-16, 0-4) erased a halftime deficit of 31-26, tying it at 41 on a Reddick jumper. Later, a 10-0 spurt - all on free throws - built an 11-point lead.
Williams finished with 13 points. Robinson had 15 with four 3-pointers.
Reddick had 11 points and seven rebounds for TSU. Jay Harris led the Tigers with 16 points and added seven boards.