The hosts got off to a quick start, taking a 19-8 lead after a pair of three-pointers from David McClure and Rokas Giedraitis.
Siauliai led by as many as 13 points, but Barsy managed to scale the deficit down to 31-38 by the halftime break.
A strong start to the second half, allowed the home side to pull away once again, as Siauliai increased the advantage to 52-33 after a 14-2 start to the third quarter.
Although Barsy had cut the gap to seven points in the fourth quarter at 57-64, Chris Cooper scored six points in a row for the hosts to seal the win.
Vytautas Sulskis was the top-scorer for the winners with 19 points, while Cooper finished the game with 17 points in 20 minutes of play.
For the guests, Mikhail Yevstigneev had a double-double of 21 points and 12 rebounds, Yevgeniy Issakov scored 13 points, as Frederick Zambalist added 12.