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In the men's section, world No. 1 Daniil Medvedev and fourth seed Stefanos Tsitsipas defused big-serving American threats Taylor Fritz and John Isner to reach the semifinals.
Second seed Anett Kontaveit also had her preparations for Flushing Meadows cut short in the round of 16.
With the win, the former world number one will re-enter the top 10 next week at number six.
The first stop on Serena Williams' farewell tour came to a quick end as she fell 6-2 6-4 to Belinda Bencic in second-round action at the Canadian Open.
The 23-year-old asking the federation to instead invest the money in promoting tennis at the grassroots-level in the country.
The favourtie, on a 37-match winning streak, was stunned by France's Alize Cornet 6-4 6-2.
The World No 1 defeated Dutch player Lesley Pattinama Kerkhove 6-4, 4-6, 6-3.
The Spaniard beat Francisco Cerundolo 6-4 6-3 3-6 6-4 in the first round.
Men's top seed and defending champion Novak Djokovic, chasing a 21st Grand Slam title after a troubled year, will open his campaign against South Korea's Kwon Soon-woo.
Djokovic and Nadal find themselves in different halves of the draw and they cannot face each other until the men's final on July 10.