Williams had taken out No.4 seed Victoria Azarenka the night before, and the after-effects of such a tough one seemed to be showing up early in this match, as the No.8-seeded Petkovic built a 6-1, 2-0 lead in less than half an hour. But the seven-time Grand Slam champion - and two-time Bank Of The West Classic champion - finally came alive, winning six of seven games to take the second set, 6-3.
Though she snuck out the second set, Williams still seemed to be playing catch-up in the third - Petkovic jumped out to a 3-1 lead, then Williams caught up to 3-all; Petkovic again jumped out to a 5-3 lead, then Williams caught up to 5-3. Petkovic's next burst gave her the match, though, as she won the next two games to finally close the former No.1 out after an hour and 49 minutes, 6-1, 3-6, 7-5.
"She played really well, and I wasn't as on today as in previous days," Williams said. "But you're going to have days like that and have to work through them. I came close, but she was just too good. She's been having a great year and she managed to play those last few games just a little bit better."
Earlier in the day an all-lefty semifinal was set, with Angelique Kerber and Varvara Lepchenko dominating a pair of WTA Rising Stars in straight sets. The No.3-seeded Kerber was the first to move through, breaking Garbiñe Muguruza in all seven of her service games - and allowing her only nine points in those seven service games - en route to a comprehensive 6-2, 6-1 victory in 56 minutes.
"It was a very good match for me," Kerber said. "I played good, aggressive tennis. I knew before the match it would be a tough one because she hits the ball very fast, so I was just trying to play point by point, and I'm happy about my game today. I'm happy I've been playing some good matches here."
Lepchenko needed even less time on court, beating fellow American - and qualifier - Sachia Vickery in just 51 minutes for her 400th career match win, 6-1, 6-0. Lepchenko is now through to the second WTA semifinal of her career, her first coming at Seoul in 2012, and because Seoul was an International-level event and this is a Premier-level event, this is the best result of the American veteran's career.
"It's obviously hard to play someone else from the United States and I know Sachia well - we've practiced together so many times," Lepchenko said. "I knew it would be mentally tough, so I really got ready for it and gave the best tennis I could. I came out as a winner so I'm pretty happy about it.
"It feels great to reach my first Premier semifinal because I've been putting so much work in."
Lepchenko leads Kerber in their head-to-head, 4-2, though Lepchenko's four wins all came before Kerber's breakthrough run at the 2011 US Open, which propelled her into becoming a top player - since then the pair has played twice and the German has won both meetings, in 2013 and this year.
Had the best experience of my life this week at Stanford even though today was disappointing. New career high ranking and 2 top 50 wins. :))