Gavin made 9 of 11 shots before the break - 5 of 7 from beyond the arc - but scored only from the foul line in the second half. Keon Johnson had 16 points and Bjorn Broman 14 for Winthrop (16-6, 8-3 Big South).
Despite Gavin's superlative first half, the Eagles led by just six at halftime, thanks to Radford's 57 percent shooting from the field.
Rashun Davis made a layup with 16:46 remaining to cap a 6-0 run for Radford (13-10, 6-5) and tie the game at 54-all, pulling even for the first time since 2-2.
The Highlanders tied twice more, but the Eagles made 9 of 10 free throws in the final 1:16.
Brandon Holcomb was 9 for 10 and scored 18 points for Radford. Davis added 15 points and five assists.