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Nadal was not troubled on Court Philippe Chatrier, and the win kept him on course to equal Bjorn Borg's record of six titles.
"I have improved since the tournament started," said Nadal, who was pushed to five sets in the first round. "I'm able to play better and I'm going to continue on this path."
Novak Djokovic also had a successful day, even though he wasn't scheduled to play. The second-seeded Serb reached the semifinals of the tournament — where he could meet Roger Federer — when quarterfinal opponent Fabio Fognini withdrew because of injury.
"Walkover from Fognini. Bad luck for him, hope he recovers fast. Today i get to enjoy Paris in a different way :-)" Djokovic wrote on Twitter.
Nadal won four straight titles at the French Open before losing to Robin Soderling in the fourth round in 2009. Nadal could face Soderling in the quarterfinals this year.
Federer won the 2009 French Open to complete a career Grand Slam, but Nadal returned to win his fifth title in 2010.
Djokovic is after his own records.
If he wins his semifinal match, he would equal John McEnroe's Open era record of 42-0 for the best start to a tennis season and clinch the No. 1 ranking. With three more victories, the second-seeded Serb will match the record of 46 straight wins set by Guillermo Vilas in 1977.
The two-time Australian Open champion has never won the title at Roland Garros, but he beat Nadal in two clay-court finals leading up to the French Open.
Fognini, who injured a muscle in his left leg while beating Albert Montanes on Sunday, announced Monday that he would not be able to play Djokovic, who is 41-0 in 2011 and has won 43 straight matches overall.
Li became the first Chinese player to reach the quarterfinals at Roland Garros after her victory over Kvitova. She will next face either No. 4 Victoria Azarenka of Belarus or Ekaterina Makarova of Russia.
"I was really in trouble," Li said about trailing 3-0 in the third set. "I didn't believe I could come back, because she has a huge, big serve. But I was OK. She had just broken once."
Based on reporting by the Associated Press.