Marque Perry had 22 points on Tuesday night for the Russian team which also got an impressive outing from Great Britain international Andrew Sullivan (13 pts and 7 rbs).
Samara's losing streak had dated back to their Qualifying Round Two second-leg setback to KK Zagreb on November 11. They won that tie on aggregate to advance to the Regular Season.
The triumph at Tartu has improved Samara's record to 1-3 in Group G while dropping the Estonian team to 2-2.
Valeriy Tikhonenko's men hit 12 of 20 (60%) from long range, a stat which proved to be decisive as Tartu hit seven less (five of 20).
The Russians would have won by an even more decisive margin had their free throw shooting not been so abysmal.
They made only 12 of 22 (54.5%) at the stripe but on this occasion, it didn't hurt their cause.
Tartu led only briefly at the start of the game after a Janar Talts lay-up.
Andrey Ivanov replied with a three-pointer and Sergey Demeshkin followed with a jump shot.
Samara ended up outscoring their hosts 21-14 in the first quarter and were on top 44-29 by half-time.
The rout was on midway through the third frame when Demeshkin's three-ball took his points tally to 16 and gave Samara a 58-36 stranglehold on proceedings.