Wofford led 27-25 at halftime and pushed that lead to 46-31 behind a Drew Crowell layup with 14 minutes left to play.
Appalachian State (10-15, 6-9 Southern Conference) rallied to cut the deficit to 59-58 after Tab Hamilton converted a four-point play but Skinner made two free throws and Loesing hit a 3-pointer to seal the win for Wofford.
Kevin Giltner had 13 and Crowell added 10 and nine rebounds for the Terriers who won the battle of the boards 39-25. Giltner was 3 of 5 from behind the arc as Wofford (16-11, 9-6) shot 43.8 percent (7 of 16) from 3-point range.
Mike Neal led Appalachian State with 15 and Hamilton chipped in with 11.
It's Wofford's fifth-straight win against Appalachian State.