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Jelena Ostapenko stunned Coco Gauff 7-5, 6-3 to reach the quarterfinals after putting on a power-hitting clinic.
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.
She also was simply outplayed by Cornet, a 32-year-old from France who beat past major champions Simona Halep at the Australian Open, Jelena Ostapenko at the French Open and Iga Swiatek at Wimbledon, ending the No. 1-ranked woman's 37-match winning streak at Wimbledon.
The US Open draw did Serena no favours, the 40-year-old American landing in the bottom quarter where fifth-seeded Tunisian Ons Jabeur, the Wimbledon runner-up, 10th-seeded Daria Kasatkina and last year's losing finalist Leylah Fernandez all lurk.
Wimbledon champion Elena Rybakina and Simona Halep also advanced.
Maria, at 34 the oldest player left in the women's draw, upset the former French Open champion, 5-7 7-5 7-5.
Ranked 103rd, the mother of two, defeated the fifth seed 6-3 7-5.
The Spaniard beat Francisco Cerundolo 6-4 6-3 3-6 6-4 in the first round.
Dokic, who became a tennis coach and commentator after her retirement in 2014, said the last six months had been tough with "constant feelings of sadness and pain".
Djokovic defeated Tsitsipas 6-0, 7-6 for his first title of 2022.