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.

“She was ready to quit,” her husband, Justin Sands, recalled. “She was like, ‘I’m done. I can’t do it. I don’t want to come back.’”

Instead, Mattek-Sands “stuck it out,” in her words, making some significant changes — to her diet after discovering a host of food allergies, to her point-to-point focus. 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 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.”

There was hip surgery less than a week after her wedding in late 2008, a torn shoulder in 2011, a broken right big toe in 2012. Her ranking plummeted from a best of 30th to outside the top 200. She found herself playing in the sport’s minor leagues and going through qualifying just to get into tournaments.

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 tournament since six made it in 2004. The five U.S. women left, out of the 15 in the main draw, are the most this far at any Grand Slam tournament since the half-dozen at Wimbledon in 2005.

“We have a lot of talented, young kids,” Mattek-Sands said, then added with a wink and a smile, “Obviously, older kids, too.”

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.

“Other than Serena, we’re all a work in progress. A couple years ago, we were not even here. And so we’ve definitely taken a step forward and we’re still progressing and still trying to make that push,” said Hampton, who beat qualifier Anna Karolina Schmiedlova of Slovakia 7-5, 6-2. “Whenever you have a big group like that, there are going to be a few that are going to rise.”

Up next for the 23-year-old Hampton is No. 7 Petra Kvitova, the 2011 Wimbledon champion. The 20-year-old Stephens, meanwhile, faces 92nd-ranked Marina Erakovic, who beat No. 16 Dominika Cibulkova 6-2, 2-6, 6-4 to become the first woman from New Zealand to reach the French Open’s third round.

Stephens, like other players on a wet afternoon, weathered two rain delays during a 6-1, 6-3 win against Vania King of the U.S. 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 Rafael Nadal against Slovakia’s Martin Klizan.

Last year’s runner-up to Nadal, 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.