R.J. Price led the Highlanders (20-10, 11-6) with 20 points. Javonte Green added 16 points, Ya Ya Anderson 15 and Cameron Jones 11. The loss ended Radford's regular-season conference title hopes with a game to go.
A basket by Anderson had the Highlanders within three, 72-69, with 1:10 left but they didn't score again as the Flames made eight consecutive free throws, four by Joe Retic.
Trailing by one at halftime, Radford took a seven-point lead with 13:22 left before Liberty responded with 13 unanswered points to go ahead for good.