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.
ESPN's Dan Dakich joins The Paul Finebaum Show to discuss the SEC's presence in the NBA Draft.
Ted Kapita was the top-rated recruit from West Virginia in the class of 2015 and recently played at DME Academy in Florida.
With the Suns drafting Tyler Ulis, they now have five guards on their roster who attended Kentucky.