Andreeva, the 19-year-old French Open champion, won her second straight Group 2 match and advanced as group winner after Svitolina earlier defeated Muchova 3-6 6-2 6-2.
The result eliminated Muchova from semi-final contention, while Svitolina will face Sabalenka in Friday's final group match with the remaining place in the last four at stake.
Sabalenka, the world number two and US Open runner-up, made the stronger start and broke Andreeva in the fourth game of a closely fought opening set to move 3-1 ahead.
Andreeva responded immediately, however, winning three consecutive games to draw level at 4-4 before breaking Sabalenka again and serving out the set.
The Russian maintained the momentum in the second set, capitalising on Sabalenka's errors to break early and race into a 3-0 lead.
Andreeva did not allow Sabalenka another game, sealing a dominant victory on her WTA Finals debut.