The senior also threw a third-quarter touchdown pass to Ja-Quan Lumas to help the Wildcats (5-1, 3-0 Mid-Eastern Athletic Conference) win their fourth game of the season decided by four points or less and third in which they trailed in the fourth quarter.
The Bulldogs (2-3, 1-1), who had 18 penalties for 144 yards, took a 14-10 lead on Antonio Hamilton's 82-yard punt return with 10:43 left. But Williams led the Wildcats on an eight-play, 51-yard drive to regain the lead in a battle between the two teams that won or shared six of the last seven league titles.
Anthony Jordan rushed for 121 yards for the Wildcats.
Caleb York threw for 175 yards and a third-quarter touchdown pass to Taquan West for South Carolina State, which had two touchdowns called back due to penalties.