Parnu had a 12-10 advantage in the first quarter, but the visitors from Lithuania finished the period with an 11-3 run to take a 21-15 lead.
The second quarter proved to be decisive in the game, as Siauliai won the second ten minute stretch by 16 points and heading into halftime up 45-27.
Nothing changed in the second half, with Siauliai continuing to make long-range shots and Parnu struggling to score.
Siauliai finished the night, making 13-of-26 three-point attempts and shared the ball extremely well, making 22 assists.
Eigirdas Zukauskas had 16 points for Siauliai, Darius Pakamanis collected 14, while Arunas Sajavicius added 9 points and 7 rebounds.
Janis Vahter was the top scorer for the losing side with 16 points and 8 rebounds, as Rannar Raap added 13 points.