Siauliai broke away to a 20-7 lead already in the first quarter after David McClure concluded a 10-0 spurt for the home side with a jumper of his own.
Although Barsy had got as close as two points in the second period, Siauliai managed to restore the double-digit advantage with a 6-0 run to finish the half.
The hosts were clearly the better side in the third quarter as well, leading by as many as 20 points on several occasions and entering the final period with a 69-51 lead.
Barsy did not want to give up easily, though. The visitors from Kazakhstan scraped the deficit to 10 points within a couple of minutes, and continuing to pile pressure on Siauliai.
With 1:23 remaining, the guests got within 78-84 as Fredrick Zambalist contributed seven points to an 8-0 run by Barsy, but David McClure stopped the run, allowing the home side to take another win.
Rokas Giedraitis and Chris Cooper scored 16 points apiece, while Vytas Sulskis finished the game with 15 points and six rebounds for Siauliai.
Fredrick Zambalist had his best game of the season for Barsy, collecting a game-high 28 points to go along five rebounds, five assists and two steals.
Mikhail Yevstigneev scored 15 points and grabbed six boards, as Lukas Brazdauskis chipped in with 12 points.