D.J. Mason's three-point play closed Campbell within 78-76 with 30 seconds left, but Price made three free throws and Javonte Green one more to guarantee Radford the No. 3 seed from the North Division in the Big South Tournament next week.
Radford (19-11, 9-6 Big South Conference) led by 16 points early in the second half and Jalen Carethers had a three-point play with 5:48 left that put the Highlanders up 69-57.
Campbell (12-18, 6-9) stormed back with a 16-4 run to tie the game at 73-73 with 2:03 left to play.
Price answered with a 3-pointer and Green made two free throws to extend the Radford lead to 78-73.
Mason and Andrew Ryan had 18 points to lead Campbell.