The Buccaneers (8-18, 6-7 Atlantic Sun Conference), who had not led since 2-0, hung on with John Walton's steal from Joel Naburgs as time expired.
ETSU, which lost to Stetson 72-70 on Jan. 10, trailed 54-34 with 12:10 remaining. Although the Hatters (10-14, 7-6) did not make another basket for 9 minutes, they still led 58-49 with 3:13 left.
Hunter Harris made a layup, Walton converted a three-point play and Rembert hit a 3 to get within a point.
After Aaron Graham, who led Stetson with 15 points, hit a 3 for a 61-57 lead with 1:29 left, Harris made another layup with 1:10 to go. Stetson missed two field goals and committed a turnover before Rembert's game-winner.