STANFORD, Calif. (AP) -- Venus Williams feels like the hometown girl when she plays at Stanford even though she grew up in Southern California and currently resides in Florida.
She has enjoyed a lot of success here, made her professional debut at the event, and the crowd was clearly supporting her.
''It's nice to have that support,'' Williams said after advancing to the Bank of the West quarterfinals Thursday night, beating fourth-seeded Victoria Azarenka 6-4, 7-6 (1).
''It was good to hear the 'oohs' and 'aahs' for both of us,'' the unseeded Williams said. ''I don't want to let anybody down. This year has been a lot more relaxing than Southern California.''
Williams and Azarenka, both former world No. 1s, are working their way back to high level tennis following injuries and illness. Williams, who is 4-0 against the Belarusian, appears slightly ahead in her development.
''It's always great to get a win against a player like Victoria, who is a champion,'' Williams said. ''We played a high level and it got better as the match went on.''
After the 10th-ranked Azarenka, who celebrated her 25th birthday, saved three match points to tie it 6-6, Williams won the first five points in the tiebreaker.
''The tiebreaker felt great,'' Williams said. ''It brought out my best tennis. I needed the challenge.''
Azarenka's second serve was the biggest difference between the hard-hitting players. She won just 32 percent of her second serves, handing Williams a significant advantage.
''We both had good points,'' Azarenka said. ''Venus was a little better on her execution on important points. I have to be realistic and look at the things that have to be done. It's not easy being patient but if I wanted easy, I'd go sit on a couch.''
Despite losing, Azarenka was glad to be playing tennis on her birthday.
''Losing is never satisfying,'' she said. ''But I left the best part of my day on the court. I was able to do something I love on my birthday.''
Williams, who reached her third quarterfinal of the season, will face eighth-seeded Andrea Petkovic on Friday.
Williams, in her 12th career appearance at Stanford, reached her 10th quarterfinal. She has won twice and finished second five times.
Azarenka won the event in 2010 and has been eliminated in the second round in her last two appearances.
''I was moving well and it was a good start,'' Azarenka said. ''I know there is work to be done and that is what I want to do.''
Fifth-seeded Ana Ivanovic also advanced, beating qualifier Carol Zhao 6-1, 6-1.
The 11th-ranked Serb, looking for her fourth title of the year, will face top-ranked Serena Williams on Friday.
''It will be a tough challenge but a good test to see where I need to work,'' Ivanovic said. ''It's a different part of the season and a different kind of tournament.''
Ivanovic will move into the top 10 next week for the first time in five years.
''I can't think too much about the future,'' Ivanovic said. ''I am looking to turn it around at the U.S. Open. After the match today I went back out on the court to get the rhythm back on my serve. That's what I need to be doing.''
Zhao, a sophomore All-America at Stanford, appeared in her second WTA Tour event and gained her first career win at the level Tuesday when Yanina Wickmeyer retired because of a viral infection.
Ivanovic, a former No. 1, had three aces and won 75 percent of her first-serve points.
In other matches, third-seeded Angelique Kerber beat Coco Vandeweghe, 7-6 (4), 0-6, 6-2, and Garbine Muguruza topped Daniela Hantuchova, 6-4, 6-4.