The result has left all side in the group with identical 2-2 records.
In a bizarre first half, Olympia fell behind 21-11 by the end of the opening quarter but then held the visitors to just six points over the next 10 minutes and led 38-27 at the break.
The Greek team began to pull away after the restart and extended the advantage to 48-32 on a lay-up by Marios Batis.
A blowout victory looked possible.
EWE Baskets held their nerve, though, and when Je'Kel Foster buried a three with 49 seconds to go in the frame, EWE Baskets only trailed 55-51.
Olympia scored the last four points of the third quarter but EWE Baskets didn't go away.
They managed to close the gap 79-75 with 53 seconds to go on Miladin Pekovic's three-pointer.
EWE Baskets had to foul, and Olympia made eight free throws the rest of the way to seal the win.
Michael King poured in 26 points and had seven rebounds for Olympia. Foster scored 22 in defeat.