Fullah scored six points and posted a block during a key 16-3 first-half run that turned a 5-4 deficit into a 21-7 advantage.
Charleston Southern (14-9, 9-3 Big South Conference) took its largest lead of the game, 58-33, on a Cedrick Bowen dunk with 13:20 left to play.
Joshua Clyburn tallied 15 points and eight rebounds, Khalid Mutakabbir added 11 points and Eric Washington chipped in 10 for Presbyterian (7-20, 4-9), which got just seven points off the bench. The Buccaneers' bench contributed 29 points in the win, led by Bowen's nine.
Charleston Southern outshot Presbyterian 45 percent (27 of 60) to 37 percent (20 of 53) and collected a 36-33 rebounding edge. The Buccaneers forced 13 turnovers, on the strength of 10 steals, and scored 14 points off those errors.
Purdue's 2016-17 prospects got a jolt Wednesday when forward Caleb Swanigan announced he will return for his sophomore season.
Clemson's Jaron Blossomgame says he is withdrawing from the NBA draft and returning to school for a final season.
Jeff Goodman logs all the coaching changes following the 2015-16 college basketball season.