Smith and Furman's Stephen Croone battled in the final minute. Croone scored Furman's last five points - pulling the Paladins from a point behind to a one-point lead, and then a 65-65 tie with 21 seconds left.
Smith, for his part, scored the last seven points for UNC Asheville (8-5). His two free throws broke a 60-60 tie, a 3-pointer with 28 seconds to play put the Bulldogs up 65-63, and his mini-run ended with the game-winner as time expired.
Kevin Vannatta scored 21 points and Smith 20 for UNC Asheville.
Croone and Devin Sibley scored 16 each to lead Furman (6-7).
Furman reeled off six unanswered points - Matt Rafferty on a jumper and a 3, and Sibley a free throw - to tie at 60-60 with under two minutes left.