The Paladins (6-4) sank 22 of 26 second-half free-throw attempts, including 16 of 20 in the final 7:11 after the Hilltoppers (4-8) cut a 45-30 deficit to five points, 56-51.
Furman, which shot 51.2 percent (21 of 41) from the field in the game, also got 11 points and seven assists from Richard Brown and 10 points from Brandon Sebirumbi. Barnes grabbed 11 rebounds.
Western Kentucky shot 36.7 percent (22 of 60) from the field and hurt itself at the free-throw line, making less than half (12 of 25) in the game.
Derrick Gordon scored 12 points and Jamal Crook and Kahlil McDonald had 11 apiece for the Hilltoppers, who came in averaging 59.7 points per game, their lowest average since the 1945-46 squad.