Chuck Ester and Greg Pryor scored 12 apiece for Chattanooga (10-2). The Mocs, who have played their last four games without leading scorer Casey Jones (12.6 per game) are off to their best start since the 1993-94 season.
Radford's Rashun Davis hit a jumper that tied the game at 61 - the first tie of the second half - with 6:55 left. Ester made two layups and Duke Ethridge hit a 3 during a 7-2 run that made it 68-63 about two minutes later and the Mocs held on from there.
Davis led Radford (7-6) with 24 points. Freshman Caleb Tanner, who had scored just 12 points all season, added 13.