Nelson hit a 10-foot bank shot with 24.3 seconds remaining to put Gardner-Webb (8-10, 1-2 Big South) ahead 54-49. Keon Moore responded with a basket with 14 seconds to again close the gap to three, but Josh Castellanos made a pair of free throws with 12.3 seconds left for the final margin.
Moore scored 20 points and James Bourne 10 for the Eagles (8-7, 2-1). Winthrop, which made 15 3-pointers in its previous game, a victory over Charleston Southern, made only 4 of 20 from long range on Wednesday. The Eagles shot 27.8 percent and missed 10 of their 27 free-throw attempts.
The victory was the first at Winthrop Coliseum for the Runnin' Bulldogs since its first season in the Big South in 2008-09.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.