The visitors from Finland broke away to a 24-13 advantage already in the first quarter, but Tarvas battled back and got within two points after an 11-2 run was capped off by Kristo Saage to make it 26-24.
Led by Benjamin Raymond, who had 13 points in the first half, Pyrinto finished the second period with a 50-41 advantage.
Tarvas’ deficit reached 17 points in the third quarter, but the Estonians battled back and got within a 11 points (80-91) with 45 seconds left.
However, the situation got much worse in terms of the second-leg perspectives for Tarvas, as Pyrinto went on to score eight points in the remaining time, increasing the gap to a game-high 19 points at the final buzzer.
Benjamin Raymond paced the Finns with 20 points, Antero Lehto scored 17 points and had six assists while Kelvin Lewis added 14 points and nine rebounds.
For Tarvas, Rait Keerles double-doubled with 21 points and 12 rebounds, Kristo Saage scored 17 points, while Silver Leppik collected 14 points and seven assists.