High Point, which had gone on a 10-0 run early in the second half to overcome a one-point halftime deficit, took a 64-62 lead on Jourdan Morris' layup with 1:34 left. But Martin hit what would be the game-winning 3-pointer on the next possession, putting Radford up 65-64 with 1:20 left.
Amir Johnson went 4-for-4 at the foul line in the final 18 seconds, his only points of the game, to cap a decisive 7-0 run to seal the win.
Joey Lynch-Flohr finished with 15 points, Martin had 12 and Artsiom Parakhouski added 11 for Radford (18-10, 15-2 Big South Conference). The win keeps Radford in first place with one game left, a home contest versus Liberty on Feb. 28.
Nick Barbour paced the Panthers (9-19, 4-13) with 25 points.