Updated

World No. 1 superstar Serena Williams and last year's runner-up Sara Errani were Tuesday's quarterfinal winners at the French Open.

Williams survived a scare against fellow former champion Svetlana Kuznetsova, while Errani ousted Wimbledon runner-up Agnieszka Radwanska in straight sets on a sun-drenched day at Stade Roland Garros.

The 31-year-old Williams held off the unseeded Kuznetsova in 6-1, 3-6, 6-3 fashion, as the American overcame a 0-2 deficit in the final set on Court Lenglen.

It looked like Williams was going to roll on Tuesday, as she cruised in the first set and a dejected Kuznetsova left the court for some attention following the stanza.

The Russian veteran, however, fought back in the second, breaking Williams three times on her way to forcing a deciding third.

The 2009 champion and 2006 French Open runner-up Kuznetsova then broke Williams to open the final set and consolidated the break with a hold for a stunning 2-0 lead. But Williams was not going to be denied on Day 10 of the fortnight, as the powerful American held and then broke back to level the things at 2-all.

Williams would wind up winning five straight games to assume control of the third, including another break in the sixth game, which ended with a brilliant forehand winner on the line by the American.

Williams served out the match, which came to an end when she stroked a final forehand winner after just under two hours of see-saw tennis.

"Yes!" she shouted when it was over.

The mighty Williams hadn't lost her serve at the 2013 French Open until Tuesday, when the 39th-ranked Kuznetsova got her four times. The American, however, broke her Russian counterpart on six occasions.

"I'm very happy to have won this quarterfinal, because the whole night I was afraid of my quarterfinal match," Williams told the crowd in French. "It was a very tough match today, but it's good for me because, I don't know, but it's very good. I am exhausted."

Kuznetsova is a former world No. 2 who has won a pair of Grand Slam singles titles and is also a two-time major runner-up.

Williams is now 7-2 lifetime against the 27-year-old Kuznetsova, who captured their previous French Open meeting in a quarterfinal here back in 2009.

The 15-time Grand Slam singles titlist Williams is currently riding a career- best 29-match winning streak and is a perfect 21-0 on clay this year. She's also 72-3 overall since a stunning first-round loss to Virginie Razzano in last year's French Open, including titles at Wimbledon, the U.S. Open and the Olympic Games.

Williams' lone French Open title came in 2002 and she will now appear in her first French semifinal since 2003. She's also the first American woman to reach the French semis since Jennifer Capriati in 2004.

On Court Chatrier, a fifth-seeded Errani knocked out the fourth-seeded Radwanska, 6-4, 7-6 (8-6), in 1 hour, 51 minutes. Errani broke Radwanska six times, while the Polish star settled for five breaks in the tough setback.

Errani improved to 2-6 lifetime versus Radwanska and is now 11-1 in Paris over the last two years, with the lone loss coming at the hands of Maria Sharapova in last year's finale.

The Bologna native has reached at least the quarterfinals in four of the last six major events.

Errani was 0-28 lifetime against top-five competition before besting Radwanska.

The 24-year-old Radwanska appeared in her first-ever French Open quarterfinal on Tuesday and was the first Polish woman to reach the quarters at Roland Garros in the Open era, which started in 1968.

Williams and Errani will square off in the semifinals on Thursday. The formidable American is 5-0 lifetime against the gritty Italian, including semifinal wins at the U.S. Open last year and in Madrid last month.

Two other quarters will be staged on Wednesday, as the second-seeded and defending champion Sharapova will face 18th-seeded fellow former world No. 1 Jelena Jankovic and third-seeded former No. 1 Victoria Azarenka will take on 12th-seeded Russian Maria Kirilenko.

Sharapova is a dominant 7-1 lifetime against the former U.S. Open runner-up and three-time French Open semifinalist Jankovic, including 2-0 in Grand Slam action, while Azarenka is 3-2 all-time versus Kirilenko, including a victory in last year's Olympic bronze medal match in London.

The Russian superstar Sharapova completed a career Grand Slam by running the table in Paris a year ago. Azarenka is the reigning Australian Open champ and U.S. Open runner-up.