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.
Predrag Krunic, EWE Baskets coach:
"Congratulations to Olympia and coach Bartzokas for winning the game. We had a good start, we played as we should but we didn't use this enough. We were bad in offense and defense at the second quarter and lost the lead. In the second half we tried to come back, played better but at the end we lost some important shots and made defensive turnovers so we were close to the score, but not close enough to win."
Giorgos Bartzokas, Olympia Larissa coach:
"It was very important win for us, because I have a lot of respect for EWE Baskets and the way they play. [They have] good players and good tactics. We move on towards our target, to qualify to the next stage and if we stay focused we can do it. We beat the two leaders of the group in a row and now everybody has the same possibilities to qualify."
Milan Majstorovic, EWE Baskets player:
"We started well in defense but in the second quarter we were not aggressive enough and made some critical mistakes. in the second half with good defense combinations we came close, but not close enough."
Panteleimon Papaioakim, Olympia Larissa player:
"We had a bad start but came back early enough. We played good basketball with an aggressive defense. We also had some bad periods in the game with unforced turnovers. EWE had some grate shots at the and but we won and we can now qualify to the next round."