Isiah Brown added a double-double with 10 points and 12 rebounds as the Buccaneers (11-7, 6-1 Atlantic Sun Conference) won their sixth straight.
ETSU trailed 57-53 with 2:15 to play before scoring seven straight. Adam Sollazzo's steal and layup capped the run and put the Buccaneers up 60-57 with 22 seconds to go.
ETSU then went 6 for 6 from the free-throw line to seal it.
The Buccaneers scored 21 points off 14 rebounds and held the Ospreys (5-12, 2-4) to 4 of 22 from behind the 3-point arc (18.2 percent).