Williams' last two tournaments didn't yield the results she wanted - second round at the French, third round at Wimbledon. But she won Stanford the last two times she was here, in 2011 and 2012, and that streak continued on Wednesday as she won her 10th match in a row at the Premier-level event.
The World No.1 not only put together a +10 differential of winners to unforced errors, 29 to 19, but she was also at her very best on the big points, converting on all three of her break point chances.
She also served up a storm, nine aces to be exact, and won 11 of 14 points when she came to net.
"I was playing a player I knew was going to be very difficult to break, so it was really important for me to be super focused on my serve today," Williams said. "I'm still taking it a match at a time though - I'm just worried about doing what I want to do and what I've been practicing on the court.
"But I wasn't feeling any nerves today. I felt good. And I felt fine physically."
Next up is either No.5 seed Ana Ivanovic or Canadian qualifier Carol Zhao, who play Thursday.
While the No.1-seeded Williams made it through to the quarterfinals, No.2 seed Agnieszka Radwanska wasn't as fortunate, succumbing to heavy-hitting lefty Varvara Lepchenko in a marathon, 6-3, 3-6, 6-4.
"The match was good, and very tight, but I don't think I served well enough today. It was the worst thing for me in the match and didn't help me at all," Radwanska said. "But overall I felt good on the court. Just the first match is always tricky, and she was a really tough opponent for the first round."
Lepchenko's win over the World No.5 was the American's first ever win over a Top 5 player.
"She's so talented," Petkovic said. "The forehand is just off the chain, and her first serve also - I think she was serving at 120mph, and at age 16 too. I'm not even serving that hard now, and I'm 26.
"But I remembered myself when I was 16. You have great shots, but you can lose your focus for a few games, and you make some wrong decisions because you just don't have that experience. I knew if I just played solid it would be tough for her. But I think we're going to be hearing a lot about her."
The only other match saw American qualifier Sachia Vickery come back to beat Monica Puig, 6-7(4), 6-2, 6-1. The 19-year-old Vickery is now through to the first WTA quarterfinal of her blossoming career.