Smith and Vannatta combined for 13 points over the final 4:25 as the Bulldogs (9-5, 2-0 Big South) rallied from one-point down, 55-54, ending the game on a 16-6 run.
Vannatta knocked down a 3-pointer that gave UNC Asheville the lead for good at 59-57 with 3:02 left. Smith added a 3-pointer and three free throws.
Longwood (4-11, 0-2) had taken a 55-54 lead on nine straight points by Tra'Vaughn White, capped by a 3-pointer with 4:36 to play. White led the Lancers with 16 points, Lotanna Nwogbo and Darrion Allen scored 13 each, Allen adding five steals.