Williams sank 7-of-11 shots from the floor and all five of his free-throw attempts for Norfolk State (18-13), which will advance to take on the top-seed North Carolina Central in Friday's semifinal round. Brandon Goode added 10 points, while RaShid Gaston grabbed 10 boards.
Jyles Smith led the Tigers (13-17) with 15 points and Deven Williams had 15 points.
Neither side managed to take control in the opening stanza as the Spartans were limited to 42.9 percent efficiency from the floor and Savannah State made good on only 40 percent of its shots from the field. Norfolk State outrebounded its opponent, 19-14, in the opening 20 minutes and took a 24-23 lead into the intermission.
The Spartans got into a rhythm offensively after the break as they drained 47.4 percent of their field goal tries and converted 13-of-17 at the charity stripe. The Tigers were held under 40 percent shooting from the floor and went 1-of-4 from beyond the arc in the second period.
Norfolk State outscored Savannah State, 18-6, in points off turnovers.