Iga Swiatek shocked her best friend, Caroline Wozniacki kept up her recovery, while Novak Djokovic escaped a major shock.
There were also significant victories for American men, boosting hopes for the country's first champion in 20 years.
The PA news agency recaps day five of the US Open in this article.
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Djokovic continued to pursue a record-tying 24th Grand Slam championship, but he had to do it the difficult way by defeating fellow Serb Laslo Djere after falling behind two sets to love.
The three-time winner Djokovic, who is attempting to match Australian Margaret Court's total of major victories, had successfully overcame such a deficit eight times in his career.
After dropping the second set, he took a break, and after winning, he said: "I gave myself a pep talk in the mirror. It succeeded.
Wozniacki story keeps going
Wozniacki completed her heroic comeback by defeating American Jennifer Brady after falling behind.
The 33-year-old Dane, who has two children and resigned from tennis more than three years ago, advanced to the second week in just her third competition since coming back to the sport.
"Playing here on Arthur Ashe again is a dream come true as a competitor and an athlete, you always want to win and you have to believe in yourself," she said.
"I thought I'd just be here watching when I retired three years ago and had two kids. What a privilege this is.
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New information from Iga Swiatek
The American dream still exists.
Since Andy Roddick won at home in 2003, the USA has been yearning for a winner, and they will undoubtedly have at least one quarterfinalist.
After defeating Alejandro Davidovich Fokina of Spain 6-1 6-0 3-6 6-3, Tommy Paul advanced to the fourth round. He will now face fellow American Ben Shelton, who defeated Aslan Karatsev of Russia 6-4 3-6 6-2 6-0.
The 10th seed, Frances Tiafoe, overcame a set deficit to defeat Adrian Mannarino of France.
Not many joyful outcomes
Taylor Fritz, a fourth American, destroyed Jakub Mensik 6-1 6-2 6-0 on the Czech qualifier's 18th birthday, dropping just three games in the process!