JOIN USLi Na, the Australian Open champion, followed her male counterpart Stanislas Wawrinka out of the French Open in the first round when she lost 7-5, 3-6, 6-1 to local favourite Kristina Mladenovic on Tuesday.
The second seed from China, who won the Roland Garros title in 2011, admitted she had handed her victory to the Frenchwoman through her own failings on another chilly day in Paris.
"I think it doesn't matter who plays today against me, I always lose the match. Today I just gave it away," said Li. "Nobody says if you're No. 2 in the world you have to win all the matches.
"The problem is myself, I don't think I'm doing well on the court. I didn't think totally what I should do, like especially I didn't follow the game plan. In my mind I didn't have any idea how to play the match."
It was the first time men's and women's Grand Slam champions have been knocked out in the following major in the first round. Wawrinka, the Swiss third seed, lost to Spain's Guillermo Garcia Lopez in four sets on Monday.
Once dubbed the next big thing of French women's tennis, Mladenovic saved two set points in the opener, lost focus in the second but stepped up a gear again in the decider to wrap it up on her second match point.
"It's incredible, without you I couldn't have done it," a weeping Mladenovic told the cheering crowd.
"When such a player comes back in the match, you know you will have to seize every opportunity."
Another young Frenchwoman, Caroline Garcia, offered far fewer problems to 2008 champion Ana Ivanovic on the same court.
The Serbian won 6-1, 6-3 to join the 2009 title winner, Svetlana Kuznetsova, in the second round.
In the men's draw, last year's runner-up David Ferrer, the fifth seed, eased through 6-4, 6-3, 6-1 against Dutchman Igor Sijsling.
Dimitrov ousted
Eleventh seed Grigor Dimitrov, one of the young players expected to challenge the likes of eight-times champion Nadal in Paris, found giant Ivo Karlovic too hot to handle in a 6-4, 7-5, 7-6 (7-4) loss.
"Today he was all over the court. He was just hitting his shots, you know, penetrating every volley, low slice, serving really good. He always serves good," said Dimitrov.
France's Richard Gasquet, seeded 12, won 6-2, 6-1, 7-5 against Austria's Bernard Tomic while former world No. 1 Lleyton Hewitt, who had reached two quarterfinals in 13 visits before Tuesday, lost 3-6, 6-2, 6-1, 6-4 to Argentine Carlos Berlocq.
Nicolas Almagro of Spain, the 21st seed, withdrew from his match against Jack Sock of the US when trailing 5-0 in the first set.
Simona Halep, seeded fourth, narrowly missed inflicting the first "double bagel" of the tournament after serving for the match when leading Alisa Kleybanova of Russia 6-0, 5-0.
But the Romanian lost concentration and gave up two games before winning on her first match point.
"I was thinking at 5-0 that I can win 6-0 6-0, but wasn't too good," Halep said. "I was a little bit relaxed after that, and it was cold."
She next plays British qualifier Heather Watson who beat Barbora Zahlavova Strycova of the Czech Republic 6-3, 6-4.
Japan's Kimiko Date-Krumm, the older stateswoman of the WTA Tour at 43, saved four match points but still went down 6-3, 0-6, 6-2 to 24th seed Anastasia Pavlyuchenkova.
American 15th seed Sloane Stephens beat China's Shuai Peng 6-4, 7-6 (10-8) and Kuznetsova, the Russian 27th seed, eased through 6-3, 6-1 against Georgia's Sofia Shapatava.
Important Results (1st round, prefix denotes seedings): Men: 19-Kevin Anderson (RSA) bt Stephane Robert (Fra) 7-5, 6-3, 6-4; Juan Monaco (Arg) bt Lucas Pouille (Fra) 6-3, 6-1, 6-4; Carlos Berlocq (Arg) bt Lleyton Hewitt (Aus) 3-6, 6-2, 6-1, 6-4; 28-Philipp Kohlschreiber (Germany) bt Pere Riba (Esp) 7-5, 6-4, 6-1; 5-David Ferrer (Esp) bt Igor Sijsling (Ned) 6-4, 6-3, 6-1; Ivo Karlovic (Cro) bt 11-Grigor Dimitrov (Bul) 6-4, 7-5, 7-6 (7-4).
Women: 15-Sloane Stephens (US) bt Peng Shuai (Chi 6-4, 7-6 (10-8); Elina Svitolina (Ukr) bt Petra Martic (Croatia) 5-0 retd; Kristina Mladenovic (Fra) bt 2-Li Na (China) 7-5, 3-6, 6-1; 27-Svetlana Kuznetsova (Rus) bt Sofia Shapatava (Geo) 6-3, 6-1; 4-Simona Halep (Rou) bt Alisa Kleybanova (Rus) 6-0, 6-2.