Roberts followed on David Robertson's missed layup and Radford missed a half-court heave at the buzzer.
Brandon Holcomb tied the game with a three-point play for the Highlanders (9-5) with 11 seconds left.
Roberts finished with 12 points, eight rebounds and three blocks and Robertson led Asheville (5-7) with 17 points. The Bulldogs surged to their largest lead at 48-40 with an 8-0 run midway through the second.
Radford took the lead seven different times but never by more than the opening 3-0. The game had 11 ties.