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.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.