Lawrence also had eight rebounds and seven assists for the Cougars (21-9, 13-4), who rebounded from a 55-52 loss to Gardner-Webb on Saturday. Charleston has won nine of its past 11 games.
Karl Cochran scored 23 points for the Terriers (12-18, 6-11), who had won two straight. Wofford is 4-5 in its past nine games after a 79-50 loss to the Cougars on Jan. 26.
The Cougars led 24-22 at halftime despite shooting 10 of 26 from the field, including 1 of 11 from beyond the arc. Charleston opened the second half with a 10-2 run -- Lawrence scored five -- and never trailed from there.
Charleston outrebounded Wofford 44-27 for a 32-12 scoring advantage in the paint.
The second annual Gavitt Tipoff Games, eight games between members of the Big East and Big Ten to be played Nov. 14-18, will feature Villanova at Purdue in the opener.
Michael Lewis is leaving his assistant coaching job at Butler to take the same position at Nebraska under Tim Miles.
College basketball fans should be excited about next season's Jimmy V Classic, an event that will feature Duke's heralded freshman class.