Trailing at halftime 27-23, Markeith Cummings scored 20 points in the second half to keep Kennesaw State (1-3) in the game.
Down 48-45, Cummings scored six straight points -- a layup, a jumper, and two free throws -- to give the Owls the lead 49-48 with 6:44 left to play.
That was the closest the Owls would get, as Radford (2-2) would outscore Kennesaw State 19-9 the rest of the way.
Radford sealed the victory from the free-throw line late.
Cummings led Kennesaw State with 31 points on 10-of-20 shooting.