Brandon Holcomb and R.J. Price scored 14 each while Green grabbed 10 rebounds for the Highlanders (13-7, 4-3 Big South).
Anderson scored back-to-back 3-pointers and Radford led 17-15, but High Point pulled ahead 28-24 on a 3 by Lorenzo Cugini and led 36-35 at halftime. Both teams shot over 50 percent and John Brown scored 11 points in the half for High Point and Tarique Thompson added 10.
Radford rallied in the second half, then led 59-56 on a jumper by Jalen Carethers. Holcomb made two free throws and a dunk amid a 7-0 run and the Highlanders led 68-61 with 1:01 left and stayed ahead.
Brown led High Point (14-5, 5-2) with 21 points, Thompson had 15 and Adam Weary 11.