The fourth seed needed just 74 minutes to dispatch the Czech world number 34, claiming a convincing 6-2, 6-2 victory. The reigning French Open champion fired 27 winners as she overwhelmed her 20-year-old opponent, who struggled to maintain consistency on serve and accumulated 20 unforced errors.
Andreeva quickly took control of the opening set, racing into a 4-0 advantage after Bartunkova recorded two double faults.
The Russian maintained her dominance throughout the encounter, eventually sealing the win on her second match point after her opponent had saved the first.
"I wanted to play aggressive today," said the 19-year-old.
"She's a very tricky opponent to play against... she sometimes manages to hit rockets out of nowhere. I tried to be brave no matter what."
She will now await the outcome of the semi-final between China's Zheng Qinwen and Belgium's Elise Mertens to discover who she will face in the title decider.
Andreeva is the highest-seeded player left in the competition following a string of surprise exits, with Elena Rybakina, Aryna Sabalenka and Coco Gauff among the prominent names already eliminated.