Joshua Montgomery scored five of his nine points in overtime as Savannah State outscored the Aggies 11-7 in the extra period and never trailed.
Williams drilled a 3-pointer with 15 seconds remaining in regulation to give the Tigers a 60-59 lead. With 4 seconds left, Savannah State's Terel Hall fouled Jeremy Underwood, who missed his first free throw but made the second to send it into overtime.
Jeremiah Hill scored 13 points and Jyles Smith added 12 points with 11 rebounds for Savannah State (11-17, 9-5 Mid-Eastern Athletic Conference).
Lamont Middleton scored 23 points to lead North Carolina A&T (8-21, 4-10), which has a five-game losing streak. Bruce Beckford scored 17 points and Denzel Keyes and Underwood each added 10 points.