Nevezis jumped ahead to a slight lead, finishing the first quarter with a 22-18 advantage, but the visitors from Kazakhstan kept close, not allowing the hosts to break away.
Valdas Dabkus had given a 37-29 edge just before the first half, but Barsy responded with three points at the other end to make it a five-point game after two quarters.
After an 8-0 run in the beginning of the third period, Brandon Callahan gave the guests a 44-42 advantage, but Nevezis slipped back in front before the start of the final period.
The lead changed hands a few times before the Lithuanians went on a 7-0 run to take an 80-72 advantage with a minute left in the game.
Valdas Dabkus paced the winners with 21 points and six rebounds, Arvydas Siksnius had 19 points and four assists, while Gintaras Leonavicius added 18 points.
For Barsy, Gytis Sirutavicius collected a team-high 17 points, while Mikhail Yevstigneev chipped in with 16 points.