PARIS -- When Serena Williams had won the final point Sunday, she paused behind the baseline to urge herself on with one last fist pump.
"Come on!" she shouted, as if her work wasn't done -- which it isn't.
Williams earned a berth in the French Open quarterfinals and extended her career-best winning streak to 28 matches by beating No. 15-seeded Roberta Vinci 6-1, 6-3.
It was her toughest test of the first week, but she swept the last 10 points and has lost only 10 games through four rounds.
"I just want every point," she said. "Every match I'm really focused for the whole period of time. I really want it every match."
The 15-time Grand Slam champion next plays 2009 French Open winner Svetlana Kuznetsova. With a victory, Williams would earn her first berth in a French Open semifinal since 2003.
She won her lone Roland Garros title in 2002.
The three other remaining Americans play Monday. Four U.S. women reached the fourth round, the most at Roland Garros since 2004.
Two-time Grand Slam champion Kuznetsova, ranked 39th but rejuvenated this year, beat No. 8-seeded Angelique Kerber 6-4, 4-6, 6-3.
Vinci tried everything to get Williams off balance. The 5-foot-4 Italian played serve and volley, attempted to chip and charge and mixed the pace of her groundstrokes, including an occasional drop shot.
"She played really smart," Williams said. "I knew how she was going to play. Some of the things she did I definitely expected, and I just had to come up with an answer."
Williams answered forcefully, whacking second serves harder than Vinci's first serves, and her persistent power proved the difference.
Serving in the opening game of the second set, Williams fell behind love-30, as if trying to make it a fair fight. She then hit an ace, kissed a forehand winner off a line, won the next point with another booming groundstroke and closed out the game with a drop-shot winner.
"It was not easy to win today," Williams told the center court crowd afterward in French, "but I'm very happy, and I'm ready for the next round."
She improved to 20-0 this year on clay. Since losing in the first round a year ago at Roland Garros, Williams is 71-3, including titles at Wimbledon, the U.S. Open, the London Olympics and the season-ending WTA Championships.
Williams first reached the quarterfinals at Roland Garros in 2001, when she was 19. Now she's 31 and the oldest player in the top 10.
"She's the best in the world so far," said Kuznetsova, who is 2-6 against Williams. "She has been playing unbelievable tennis. But I believe that I have game and my good days as well. Let's cross fingers I will have a good day."
Kuznetsova won when they met in the 2009 quarterfinals at Roland Garros and went on to the title.
The Russian has now reached the final eight in back-to-back major tournaments for the first time since that year. She made the quarterfinals at the Australian Open in January before losing to eventual champion Victoria Azarenka.
"Grand Slams always bring the best out of me," Kuznetsova said. "It just comes naturally. Here it's the French Open -- it says everything."
Kuznetsova whacked a forehand winner on match point, then let out a jubilant scream. She improved to 12-2 this year in three-set matches, and her winning percentage of .820 (41-9) at Roland Garros is the best among active players.
The Pole converted five of her nine break-point opportunities to reach the last eight at Roland Garros for the first time.
The 14th-seeded Ivanovic has now lost seven straight matches to Radwanska, who next plays last year's runner-up, Sara Errani of Italy.
Errani outlasted Carla Suarez-Navarro to win 5-7, 6-4, 6-3. The Italian, who lost last year's final against Maria Sharapova, had to take a medical timeout near the end of the first set after doubling over in pain and holding her stomach.
After a few minutes of treatment, the 26-year-old resumed playing but soon lost the first set.
She eventually won on her second match point with a neatly played backhand drop shot and then screamed in delight.
The match lasted 2 hours, 29 minutes and featured 13 breaks of serve.
Information from The Associated Press was used in this report.