The Governors (3-3) trailed 37-34 at halftime before taking the lead for good on Ed Dyson's dunk with 13:36 left. They built the lead to 12 points with 4:12 left.
The Bobcats (1-4) nibbled at the lead and closed within three, 75-72, on Marcus Colbert's 3-pointer with 25 seconds left. But the Governors' Preston Herring had a dunk and Damarius Smith a free throw while MSU didn't score again.
Williams made 11 of 14 free throws, including nine in the second half for the Governors, who were 27 of 42 from the line. MSU made 12 of 15. Smith added 16 points for Austin Peay.