N.C. Central (1-3, 1-1 Mid-Eastern Athletic) reached the Wildcat 1 inside the final minute, but an apparent touchdown run was ruled short, and Elliott Miller blocked Nigel Macauley's 18-yard field goal attempt to preserve the win.
Bethune-Cookman (4-1, 2-1) won its third game by four points or less this season.
North Carolina Central scored three unanswered touchdowns in the third quarter to turn a 7-6 halftime deficit into a 26-7 lead. But Williams hit Jawill Davis for two touchdown passes, and Michael Jones scored the game-winner on a 6-yard run with 10:50 remaining.
The game was moved up two hours as North Carolina declared a state of emergence ahead of Hurricane Joaquin.