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The defending champions defeated the Brazilian 6-2, 7-6(7) to set up the title match with Karolina Muchova.
The defending champion won 6-4, 6-2 against her American opponent.
The top seed won 6-0, 6-0 against China's Wang Xinyu in the third round.
Elena Rybakina also booked a third round spot with a 6-3, 6-3 victory over rising Czech teenager Linda Noskova.
While Swiatek won it for a second consecutive time, it was Sabalenka's third straight loss in the final in Stuttgart.
Jelena Ostapenko stunned Coco Gauff 7-5, 6-3 to reach the quarterfinals after putting on a power-hitting clinic.
Tsitsipas will next take on Italian Jannik Sinner in what could be a tricky test.
Garcia, 29, was ranked outside the top 70 in mid-June but has since won four titles, made the semifinals of the US Open and will now rise to a career-high No. 4.
She outlasted Kasatkina in a 32-point rally for match point.
Swiatek, who improved to 2-0 in this year's competition following her own 6-3, 6-2 win over Caroline Garcia, goes through as the winner of her group, while Gauff can no longer qualify for the semifinals.
Results 31-40 of 58
