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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.
The win continues a phenomenal season for Swiatek, who rose to world No. 1 in April and has won eight titles, including two Grand Slams at Roland Garros and Flushing Meadows this year.
She will join Iga Swiatek, Ons Jabeur, Jessica Pegula, Coco Gauff, Caroline Garcia, Aryna Sabalenka and Daria Kasatkina at the season finale.
'I struggled to win my first WTA title. It took me time. So I believe this will take me time,' said the Tunisian.
It was twice French Open champion Swiatek's first major title on a hard court and the 21-year-old is the first Polish woman to win the US Open.
After a sluggish start, the Pole came alive in the second set and overcame an early break in the decider by winning the final four games to see off the powerful Belarusian.