The sides finished the first quarter tied up at 14-14, with the guests jumping ahead 28-26 at the halftime break.
Maks&Moorits started the second half much more successfully, going on an 8-0 run to take a 34-28 advantage.
The Estonians led by as many as nine points in the third quarter, but Caspiy won the final period 19-10 and earned a hard-fought victory.
Kris Richards paced the guests with 17 points, nine rebounds and five assists, David Nesbitt added a double-double of 10 points and 12 board, while Azim Yagodkin added nine points.
For Valga, Ferm Myrick had a team-high 15 points, also collecting a game-high 13 rebounds, while Kristjan Evart was the only double-digit scorer with 14 points.