Halfway through the first quarter, the teams were tied at 10-10, but Rait Keerles scored six points in a row to ignite a 17-3 stretch, as Tarvas finished the period with a 27-13 lead.
Tallinna Kalev had cut the deficit to a mere three points (41-38) at the halftime break, but Tarvas shot ahead once again in the third quarter.
With four minutes left in the game, the guests were behind by 12 points, but a 9-2 spurt saw them get within five points with 30 seconds left.
However, Maris Laksa, who finished the game with 21 points, and Giedrius Gustas, who added 12 points and six assists, made a free-throw each to seal the game.
Rait Keerles added 18 points, five rebounds and four points for Tarvas.
Reimo Tamm had a game-high 28 points for the losing side, while Renato Lindmets and Kaido Saks chipped in with 11 apiece.