Jamal King's 3-pointer with 7:44 left gave Winthrop (18-7, 12-0) a 60-50 lead before the Lancers went on an 18-6 run and led 68-66 on Heru Bligen's layup with 2:02 left.
Falden followed with a pair of free throws to tie it and Burns and Hunter each made 1 of 2 from the foul line to secure the win.
Longwood (9-16, 4-8) failed to complete the comeback after Bligen's layup as he turned it over on the possession following Falden's foul shots with 91 seconds to go.
Shabooty Phillips missed an off-balance shot attempt with 46 seconds remaining, Chase Claxton blocked Phillips' layup attempt with 10 seconds left, JaShaun Smith stepped out of bounds with the ball with four seconds to go and Sean Flood failed to get a shot off as time expired.
Juan Munoz scored 24 points and Smith 15 for the Lancers.
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