(CNN) -- Serena Williams became the first woman through to the semifinals of the season-ending WTA Championships on Thursday, winning her third successive match in Istanbul.
The world No. 1 trounced former Wimbledon champion Petra Kvitova 6-2 6-3 in just 72 minutes to secure top spot in the Red Group.
The American has now won her past 13 matches at the event, passing Chris Evert to have the second-best unbeaten streak behind Martina Navratilova's 21 in a row from 1983 to 1987.
"I feel pretty good -- I was really aggressive tonight," Williams said after extending her career record to 5-0 against the fourth-seeded Czech, firing 27 winners -- with 11 aces -- and making just 13 unforced errors.
"Petra was aggressive too, but I think my serve did really well. I'm just glad to still be alive in the tournament -- I didn't have any expectations coming here, I just wanted to come here and enjoy myself, and that's what I've done.
"It just feels good to not be out of the tournament."
However, Polish third seed Agnieszka Radwanska is out after losing 6-2 6-2 to Angelique Kerber.
The German now has a 1-1 record, as does Kvitova, ahead of their winner-take-all clash on Friday.
In the White Group, Li Na is "one foot" away from making another piece of tennis history.
Already the first Chinese player to win a grand slam singles title, and the first to be ranked in the top five, she will now seek to reach the semifinals of the WTA Championships for the first time.
Two previous attempts have ended in disappointment, going home with a 1-2 record on each occasion, but the 31-year-old is in touching distance this year after winning her second successive match in Istanbul.
"It was tight, but at least it's better than the last two years, because now I've got one foot in the semis -- but another foot still out of the door, so I have to see how it goes tomorrow," she said.
Li faces world No. 2 Victoria Azarenka in her final round-robin match, and may still go through even if she loses -- depending on the result of Friday's other White Group clash between Jelena Jankovic and Sara Errani.
Li beat Jankovic 6-3 2-6 6-3 on Thursday in the first match this week to go to three sets, leaving Serbia's former world No. 1 with a 1-1 record ahead of her final match against Errani -- who is out of contention following two defeats.
Azarenka, who beat Li in January's Australian Open final when she was the top-ranked woman, also has a win and a loss.
The Belorussian has won their past five encounters, including at the WTA Championships in 2011 and 2012, but has been in poor form recently with just one win in four matches since losing the U.S. Open final to Williams.
Meanwhile, Grigor Dimitrov -- known earlier in his career as "Baby Federer" -- will face the real thing in Friday's quarterfinals at the Swiss Indoors event.
The Bulgarian, who claimed his first ATP Tour title in Stockholm last weekend, earned a clash with 17-time grand slam winner Roger Federer by beating Alexandr Dolgopolov 6-3 6-2.
Defending champion Juan Martin del Potro set up a clash with French qualifier Paul-Henri Mathieu, while Edouard Roger-Vasselin and Daniel Brands also went through to the last eight.
World No. 3 David Ferrer reached the quarterfinals of his home Valencia Open, where he will play fifth seed Jerzy Janowicz, but American No. 4 John Isner was upset by Frenchman Jeremy Chardy.