Serena Williams moved with a victory of becoming the oldest top-ranked women's player, sweeping aside Urszula Radwanska 6-0, 6-3 on Thursday to reach the Qatar Open quarter-finals. If the 31-year-old Williams reaches the semi-finals by beating seventh-seeded Petra Kvitova she will return to No. 1 for the first time in 2½ years. Chris Evert was No. 1 in 1985 while just shy of her 31st birthday.

"It's awesome," Williams said. "Since I didn't do the youngest, I figure I'll do the oldest."

If Williams doesn't make the last four, Australian Open champion Victoria Azarenka can keep the top spot by reaching the final. Third-ranked Maria Sharapova can pass both players if she wins the tournament and Williams and Azarenka lose their next matches. Williams, a 15-time Grand Slam winner, was joined in the last eight by Azarenka, former No. 1s Caroline Wozniacki and Sharapova, plus 2011 U.S. Open champion Samantha Stosur and Agnieszka Radwanska.

Azarenka extended her unbeaten run in 2013 to 11 matches by thrashing Christine McHale of the United States 6-0, 6-0, Wozniacki downed Mona Barthel of Germany 7-6 (6), 6-3, and Sharapova got past Klara Zakopalova of the Czech Republic 6-3, 6-3. Stosur edged Svetlana Kuznetsova 6-4, 7-5, and Agnieszka Radwanska beat an error-prone Ana Ivanovic 6-1, 7-6 (6).

On the back of her potent first serve, Williams broke Urszula Radwanska, the sister of Agnieszka, three times in the first set. The second set was tighter but the American won the match when her opponent hit a return wide.

"It was very windy but I felt good out there. It was very tough conditions," said Williams, who hurt her ankle and back at the Australian Open.

Azarenka broke three times in each set on the back of her powerful forehand and dominant net play.

"I felt like I came out very focused and really with a good mindset, with a good game plan, said Azarenka, who won 26 straight matches to begin 2012.

Sharapova is bidding to become the first player to win three times in Qatar - an honor that would be rewarded with a diamond-encrusted tennis ball.

"It's one of those days where you almost know that you might not be playing your best tennis. I certainly didn't today," said Sharapova, who had 27 unforced errors and nine double faults.

The fourth-ranked Agnieszka Radwanska made quick work of Ivanovic, the former No. 1 from Serbia, in the first set, breaking four times amid windy conditions. Ivanovic didn't help her own cause, committing 21 unforced errors and only landing 63 percent of first serves.

"She really start to play much better in the second set, and I think she didn't make any easy mistakes," said Agnieszka Radwanska, who improved to 15-1 this year after winning tournaments in Sydney and Auckland and reaching the Australian Open quarterfinals. "I really need to just play my game. She didn't give me any free points in the second set. It was really close."

Wind also played havoc for Wozniacki and Barthel. The first set swung back and forth, but the Dane took control in the second set by breaking twice to lead 5-1.

"It wasn't great tennis out there today, the wind was a huge factor," Wozniacki said.