Kournikova, 21, has endured a miserable run since she burst onto the WTA Tour in 1997.
"I just kept fighting for every point, " Wozniacki told the official WTA Tour Web site.
"I wasn't nervous before the match today, I was excited, " Li told the WTA Tour website.
Bartoli, meanwhile, reached her first WTA final in two years after thrashing Belgium's Yanina Wickmayer.
There are two tours, the ATP for the men and the WTA for women.
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"I definitely knew about it, " Serena told the WTA Tour official Web site www.sonyericssonwtatour.com.
Meanwhile, Samantha Stosur of Australia won her second title on the women's WTA Tour circuit on Sunday.
She won the Hobart WTA tournament in January before reaching the third round at the Australian Open.
Vandeweghe defeated Italy's Tathiana Garbin 6-4 6-4 for her first victory in a WTA Tour main-draw match.
The defeat effectively ends Schnyder's hopes of playing in the season-ending WTA Championships in Madrid next month.
She merely exhales when she strikes the ball, rather than loudly grunting like many of her WTA colleagues.
The 31-year-old also beat Azarenka in the U.S. Open final and at the season-ending WTA Championships in Istanbul.
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The Wimbledon women's singles seedings reflect the current WTA Tour rankings, with world number one Sharapova selected top.
Sharapova later pulled out of this week's WTA tournament in Montreal after suffering the injury to her foot.
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At the WTA event in Paris, France's Marion Bartoli will face Germany's Angelique Kerber in the final on Sunday.
Wozniacki, who has 20 WTA titles to her name, is now hoping to bounce back in Miami next week.
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The 20-year-old Azarenka has now lost five of her eight WTA Tour finals.
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"I felt good out there today, " Clijsters told the WTA Tour Web site.
While Williams continues to dominate the WTA Tour, no American man has reached the past five Grand Slam quarterfinals.
"I was happy to have a quick match, " Radwanska was quoted as saying on the WTA Tour's official website.
They have won several WTA doubles titles, including Wimbledon 2006 and the bronze medal at the 2008 Beijing Olympics.
"I'm really glad how I played today - it was a great match, " Kvitova told the WTA official website.
The 26-year-old's last win on the WTA Tour was in Stanford that year.
But Ivanovic admitted the competition on the WTA Tour is fierce in 2012.
Pavlyuchenkova could offer little response to nine aces and 24 winners as Williams claimed her 47th career WTA title.
"I don't know if I feel better on clay this year or last year, " Williams told the WTA Tour website.
"I wasn't really there, my feet weren't moving -- I don't know what happened, " she told the official WTA website.
In Malaysia, Karolina Pliskova won her first WTA singles crown after defeating Bethanie Mattek-Sands 1-6 7-5 6-3 at Kuala Lumpur.
"I didn't do much wrong today besides the first few games on my serve, " Ivanovic, 24, told the WTA's website.
It was the second time in three weeks that former junior Wimbledon champion Robson had qualified for a WTA event.
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