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Alcaraz came dangerously close to relinquishing his crown but lived to fight another day with a 5-7 6-2 4-6 7-6(2) 6-2 win.
The 22-time Grand Slam champion overpowered Kubler in 83 minutes to book his place in the last eight.
The former US Open champion is recovering from surgery on her wrists and ankle.
The honour comes a little more than a year after she shocked the sporting world when she became the first qualifier to win a Grand Slam by clinching the US Open.
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.
Second seed Anett Kontaveit also had her preparations for Flushing Meadows cut short in the round of 16.
The golden girl of Britain suffered a 6-3, 6-3 loss in the second round.
The 19-year-old lost to Aliaksandra Sasnovich of Belarus 3-6, 6-1, 6-1.
Bromley Magistrates' Court convicted Amrit Magar after he was captured several times on door camera footage at the 19-year-old player's house in south London, where she lives with her parents.
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