The win was the first conference win of the season for the Citadel, snapping a four game Southern Conference losing streak and a six game losing streak overall.
Henry also added 10 rebounds and P.J. Boutte had 14 points for The Citadel (8-10, 1-4).
The Bulldogs led by double digits much of the second half, and a Henry free throw gave them an 87-77 lead with 36 seconds left.
But a Daniel Fowler 3-point play sparked a 7-0 Furman run which, after a pair of Devin Sibley free throws, trimmed the lead to 87-86 with four seconds left. Two Boutte free throws however pushed it back to three and sealed the game.
Stephen Croone had 22 points for Furman (9-10, 3-3).