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.
“I’m even happier than I was after my first match. I feel like I could play another two matches. I’m so full of energy. I’m so pumped up. I’m so happy," Andreeva said.
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.