|Aliaksandr Kudrautsau led Tsmoki-Minsk with 19 points|
Tsmoki-Minsk came through at the finish, 81-72, to boost their hopes of reaching the last 16 of the EuroChallenge and end those of Apollon.
Having led a close game for most of the second half, Minsk looked to have blown it when Apollon - needing a win to stay alive - went on a 14-0 tear that spanned the third and fourth quarters and put them up 65-59.
But Minsk responded with an 11-0 spurt of their own to re-establish control and see it through to the close.
Minsk appeared in control when they went 50-40 up on Dzianis Korshuk's jump-shot.
Apollon would come storming back, and Diego Kapelan's three-pointer made it 65-59 with 6:49 to go.
But from there to the finish, Minsk outscored them 22-7 to take the win.
The 11-0 run was capped by three-point plays from Kudrautsau, the first a lay-up and free throw, the second a shot drilled from long-range.
That put them up 70-65, and they held Apollon at arm's length the rest of the way, helped by key three-pointers from Aliaksei Trastsinetski and Jajuan Smith.
Kudrautsau led Minsk with 19 points while Korshuk had 16 and Smith 15. Trastsinetski and Aliaksei Laskevich collected 11 points each, with Laskevich adding 11 rebounds.
Brandon Brown led Apollon with 17 points, with Dorde Lelic and Gerald Robinson adding 13 apiece.