CHARLESTON, S.C. (AP) — Laura Siegemund of Germany beat Venus Williams 6-4, 6-7 (3), 7-5 on Wednesday to win her second three-set match in three days and move on to the third round at the Volvo Car Open.

Down match point in the second set, Williams broke Siegemund as she served for the match and rallied to easily win the ensuing tie-breaker to set up the decisive third set. Williams was poised to complete the comeback, but Siegemund twice pulled back from a break and saved two match points as Williams served for the victory at 5-4, winning the final three games to reach the round of 16.

"I tried to keep up the pressure and tried to dominate the game as well as I could," Siegemund said. "I think I worked my way well through the match. It was a close match, you know, it can go either way. I just tried to believe in my game, and if I was down, I told myself I was going to get more chances."

Williams could only ponder what might have been.

"I tried my best to think this could be the best match she'll ever play in her life, honestly," Williams said. "I basically won the match but still lost."

Elsewhere, Russian Daria Kasatkina outlasted Puerto Rican Olympic champion Monica Puig 6-0, 6-7 (3), 6-2, and Shelby Rogers upset Madison Keys 4-6, 6-1, 6-1.

"I mean, she was all over my serve today," Keys said. "I felt like that let me down, and I think she served well. And I feel like I just stopped doing what I should have. I feel like I did a pretty good job to get back in the first set, and I feel like I just stopped doing it. Then it kind of all slipped away from me pretty quick."

Kasatkina, who came close to making the semifinals here last year, hit 19 winners with 18 unforced errors to finally escape after just over 2 hours on court. Puig hit more winners (25) but also had 41 errors, including on match point.

In other matches, Latvia's Jelena Ostapenko defeated Greece's Maria Sakkari in three sets and Hungarian Fanny Stollar stunned No.4 seed Elena Vesnina, 7-6 (7), 7-6 (3). Vesnina, of Russia, twice led a by a break in the opening set but struggled to convert break points. Stollar hit 13 aces to keep in front for most of the match.

Also: Anastasija Sevastova of Latvia, defeated Germany's Andrea Petkovic 6-3, 6-4; Ons Jabeur of Tunisia, defeated Magda Linette of Poland 6-4, 6-4; Daria Gavrilova of Australia defeated American Alison Riske 6-3, 6-1; Kiki Bertens of the Netherlands defeated Kateryna Bondarenko of Ukraine 6-2, 7-5; Mirjana Lucic-Baroni of Croatia defeated Mona Barthel of Germany, 6-3, 6-2; Japan's Naomi Osaka defeated Zhang Shuai of China 6-4, 6-4; Anastasia Rodionova of Australia defeated Sara Errani of Italy 6-2, 6-2; Irina-Camelia Begu of Romania, defeated Kristina Kucova of Slovakia 4-6, 6-2, 7-6 (6); Lucie Safarova of the Czech Republic defeated Bethanie Mattek-Sands of the United States 6-3, 6-3.