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.
Indiana guard James Blackmon Jr., who averaged 15.8 points in 13 games before being injured last season, has withdrawn from the NBA draft.
Isaiah Briscoe has decided to withdraw from the NBA draft and will return to Kentucky for his sophomore season. Marcus Lee intends to transfer.
The Big 12/SEC Challenge will again feature Kansas and Kentucky, this time at Rupp Arena. That's not the only exciting matchup in next season's midseason conference showdown.