Derrick Henry scored 15 points, Keon Moore had 13 and Duby Okeke 12 for Winthrop (8-8, 3-2 Big South Conference). The Eagles made 52.8 percent of their field goals, including 7 of 16 from 3-point range.
The Eagles led by as many as 20 points after Johnson's layup with 17:16 left.
UNC Asheville had won its previous seven home conference games.
Winthrop broke out to a 38-21 lead at halftime behind Johnson's 15 points. Asheville was held to eight first-half field goals and scored just seven points in the final 12:42 of the half.