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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.
Sakkari battled past world No. 3 Pegula 7-6(6) 7-6(4) to record her first win over a top-five opponent this year.
She will join Iga Swiatek, Ons Jabeur, Jessica Pegula, Coco Gauff, Caroline Garcia, Aryna Sabalenka and Daria Kasatkina at the season finale.
Greek fourth seed Sakkari kept alive her hopes of making the Finals by surviving an early scare and fighting back from a set down to beat American Danielle Collins 5-7, 6-3, 6-3.
Not since Andy Roddick in 2003 has a US man won the title at Flushing Meadows and the pressure was on for the 24-year-old Frances Tiafoe to build on his stunning win over second seed Rafa Nadal in the fourth round.
Karen Khachanov stood on court, arms raised, basking in a rowdy crowd’s cheers after reaching his first Grand Slam semifinal at the US Open.
Alcaraz, last year's quarterfinalist, remained on course for another memorable run at Flushing Meadows after squeezing past 2014 champion Cilic to set up a showdown against Jannik Sinner.
Kyrgios, Wimbledon finalist this year, has recorded the most wins on tour since the end of the French Open and continued the finest season of his career with a 7-6(11), 3-6, 6-3, 6-2 victory over Medvedev in a blockbuster fourth-round clash.
No. 12 Coco Gauff and 20th-seeded Madison Keys set up a third-round match-up.