Devin Sibley added 20 points for the Paladins (13-10, 7-3 Southern Conference), who led 72-57 with 3:56 to play before having turnovers on five straight possessions.
T.J. Cromer started the Buccaneers' rally with a 3-pointer at 3:30 and ETSU made five of six free throws, closing within 72-70 with 1:31 left.
The Bucs had two shots in the final minute to tie or take the lead before a Croone rebound gave him a chance to ice it.
Cromer had 22 points and Ge'Lawn Guyn 19 for the Bucs (13-9, 6-3).
Sibley and Croone combined for 23 points in the first half as Furman took a 39-27 lead. The Bucs were within six before two baskets from Sibley capped an 11-1 run to make it 68-52 with 5:56 to play.