Mike Burwell chipped in 10 points and Bilal Dixon grabbed 10 rebounds for the Tigers (1-1).
Javonte Green and Ya Ya Anderson scored 10 points apiece for Radford (1-2), and three players scored eight points—Rashun Davis, R.J. Price and Kion Brown.
Towson dominated Radford on the boards, outrebounding the Highlanders 43-24. The Tigers also had 10 steals.
Towson led 33-24 at the half, but pulled away to a 40-26 advantage with 16:49 to go. They led 66-50 with 5:10 left.
Towson allowed Radford to stay in the game with its poor free-throw shooting, managing only 42.9 percent (12 of 28), but Radford could get no closer than seven down the stretch.