Davis scored 15 points in the second half and dished out five assists. Anderson hit four 3-pointers and finished 7 of 12 from the field.
Radford (17-9, 7-4 Big South) is tied with Virginia Military Institute for the top spot in the North Division. UNC Asheville (13-12, 7-4) drops into a three-way tie in the South.
Jaron Lane scored to cap a 22-10 run, pulling Asheville within a point at 71-70 with 8:54 to play. Davis answered with six points, and a Kion Brown layup stretched the lead to 79-72 and the Bulldogs would not get closer.
Freshman guard Andrew Rowsey scored a career-high 41 points on 14-of-28 shooting to lead UNC Asheville (13-12, 7-4).