With the Paladins (8-9, 2-4 Southern Conference) ahead 58-56 with less than three minutes to go, Bostain and Webb hit back-to-back 3-pointers in 17 seconds to stretch Furman's lead to eight.
The Terriers (5-13, 0-7) again cut the deficit to two on Drew Gibson's layup with 38 seconds to go. But Bostain hit a pair of free throws with 9.2 seconds left to seal the win.
Furman had 44 rebounds to 28 for Wofford, but the Terriers had 11 steals and forced 15 Paladin turnovers.
Shane Nichols scored 19 points and Gibson added 17 points and six rebounds for Wofford, who has lost 12 of its last 13 games.