There were moments, as recently as last year, when a body that would not stay healthy and on-court results prompted Bethanie Mattek-Sands...

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PARIS — There were moments, as recently as last year, when a body that would not stay healthy and on-court results prompted Bethanie Mattek-Sands to wonder whether it was simply time to call it a career after more than a decade as a professional tennis player.

Instead, Mattek-Sands “stuck it out.” And at age 28, in her 27th Grand Slam tournament, Mattek-Sands earned her most significant victory to date, a 5-7, 6-3, 6-2 upset of 2011 champion Li Na of China at the rain-soaked French Open on Thursday to join four other American women in the third round.

“I know how I can play, and, you know, there were times when I just physically couldn’t do it,” the 67th-ranked Mattek-Sands said, “and I think that’s really frustrating.”

By beating the sixth-seeded Li to earn her fourth career win in 25 tries against top-10 players, Mattek-Sands helped give the United States its largest group of women in the third round at the clay-court Grand Slam since six made it in 2004. The five U.S. women left are the most this far at any Grand Slam tournament since the half-dozen at Wimbledon in 2005.

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The other Americans in the third round: No. 17 Sloane Stephens and 54th-ranked Jamie Hampton, who also won Thursday, and No. 1 Serena Williams and No. 29 Varvara Lepchenko, who won Wednesday.

Hampton beat qualifier Anna Karolina Schmiedlova of Slovakia 7-5, 6-2. The 20-year-old Stephens beat American Vania King 6-1, 6-3.

Only 18 of 32 scheduled singles matches were completed, with two-time Australian Open champion Victoria Azarenka and 2011 U.S. Open champion Sam Stosur among the winners. Six were suspended in progress — defending champion Maria Sharapova led Canada’s Eugenie Bouchard by a set and a break when they stopped — and eight were postponed entirely, including seven-time French Open title winner Rafael Nadal against Slovakia’s Martin Klizan.

Top-ranked Novak Djokovic gestured at the dark, threatening sky between points, as if to admonish the clouds for even considering halting play before he could finish a 6-2, 6-0, 6-2 victory over 83rd-ranked Guido Pella of Argentina.