The hosts got off to a superb start, taking a 15-6 lead six minutes into the game after Ernestas Ezerskis drained a three-pointer. However, Dynamo rebounded after a poor beginning of the game to finish the opening quarter trailing only 14-17.
The Russian side took the over the initiative in the second quarter, going up 33-27 after Alimadzan Fediushin made one-of-two from the free-throw line, but the Estonians responded with a quick 5-0 run and only one point separated the sides at the interval at 32-33.
Teams exchanged leads in the third quarter, but the Moscow club maintained a slight advantage, entering the final quarter of play with a 52-50 edge.
However, Tyco Rapla had the last say in the game, taking a 63-57 lead midway through the final frame after a 6-0 run and held on to the advantage until the final buzzer.
Rait-Riivo Laane led the winners with 19 points, Rait Keerles collected 14 points, while Martin Paasoja collected 12 points for the Rapla team.
Meanwhile, Denis Zakharov was the leading scorer for Dynamo, with Alexey Kuznetsov and Bendzhamin Dudu chipping in with 11 points each.