Johnson and Davenport also contributed five rebounds each for the Eagles (13-6, 5-3 Big South). Xavier Cooks and Jimmy Gavin added nine points apiece. The team shot 49.2 percent from the field and 69.2 percent from the line.
Duby Okeke made three consecutive dunks late in the first half to help Winthrop close a 21-10 deficit, but Gardner-Webb held on for a 33-25 advantage at halftime.
Johnson contributed 10 points to a 19-8 surge to open the second half that gave the Eagles a 44-41 lead with 12:32 to play. Cooks sank back-to-back 3-pointers to extend Winthrop's lead to 61-50 with 6:25 to play and the Eagles cruised from there.
Dylan Poston had 15 points with two assists and three rebounds for the Bulldogs (10-10, 5-3).