After a promising start, Barsy finished the first quarter with an 18-16 advantage, with Harrison knocking down a three-pointer as the opening period concluded.
The guests led had increased the gap to six points (22-16), but a 17-3 run saw Siauliai turn the game around completely to take a 33-25 lead halfway through the second quarter.
Having finished the first half with a 39-37 edge, the hosts turned up the intensity in the third and fourth quarters, scoring 68 second-half points and running away with an easy victory.
Rokas Giedraitis, Julius Jucikas and Travis Leslie all finished with 21 points apiece for the winners, with Leslie also adding 10 rebounds and six assists.
For Barsy, Lithuanian swingman Gytis Sirutavicius collected a team-high 17 points, Bryan Harrison scored 14, while Fredrick Zambalist chipped in with 11 points.