Michael Obacha, Jay Canty and Mike Neal each scored 14 points to help Appalachian State (11-13, 7-6) win for the third time in four games.
Trailing 64-60 at the 2:30 mark, Larry Wideman made a 3-pointer for Furman (6-17, 3-9) to cut the lead to one, 64-63 with 1:31 left to play. That was the closest the Paladins would get.
Canty converted a three-point play for the Mountaineers on the ensuing possession to extend the lead to 67-63 with 1:07 remaining.
Appalachian state made 5 of its last 6 free throws to close out Furman.
The Mountaineers led by as many as 18 points, while the Paladins never led.
Furman, which has lost four in a row, was led by Stephen Croone with 20 points.