It was the first victory in nine matches against opponents ranked in the top 10 for Nara, who is No. 116.
"Biggest win of my career," she called it.
Nara has never been past the third round at any Grand Slam tournament.
She arrived in New York having a rough season, failing to qualify at any of her past three events. She also was 4-11 in 2017 before this week.
But Nara broke in six of Kuznetsova's 13 service games and was steady down the stretch.
"I was nervous," Nara said, but figured that her decision to play aggressively and try to move into the court as much as possible helped her.
The No. 8-seeded Kuznetsova's exit means five of the top eight women in the field are already gone before the third round. She joins No. 2 Simona Halep, No. 5 Caroline Wozniacki, No. 6 Angelique Kerber and No. 7 Johanna Konta. Kerber was the defending champion.
In addition to her U.S. Open title, Kuznetsova was the runner-up in 2007. She also was the French Open champion in 2009.
The Russian came to New York this year as one of eight women with a chance to move up to No. 1 in the WTA rankings after the tournament.
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