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Swiatek will next face Sabalenka in the semifinals, while Gauff will lock horns with Pegula for a place in the final.
American Pegula booked a semifinal spot at the season-ending tournament with a 6-3, 6-2 victory over Sakkari.
All four players in the group can reach the semifinals.
Pegula, who came into the contest with a dismal 1-4 record against the hard-hitting Sabalenka, managed to absorb her powerful serve to extend rallies and thwart the Belarusian's comeback attempts.
Swiatek completed the first set comeback on a double fault and a disillusioned Vondrousova went quietly in the second set.
Pegula won 10 of the last 12 games to get past an error-prone Rybakina and notch up a 7-5, 6-2 win.
The 31-year-old former Wimbledon and French Open champion had been provisionally suspended since October 2022 after testing positive for banned blood-booster roxadustat at the US Open last year
Sabalenka faces China's Zheng, who knocked out 2022 finalist Ons Jabeur, in the qusarterfinals.
Having retired in 2020 to raise a family and playing in just her third event since returning to action Wozniacki turned back the clock to come out on top in the battle of 33-year-old Grand Slam champions.
Samsonova had to play the match about two hours after upsetting third seed Elena Rybakina in a rain-postponed semifinal clash meant to be played on Saturday.