Roger Federer and David Ferrer remained on course for a quarterfinal clash in the men's singles but women's top seed Wozniacki was thrashed 6-1, 6-3 by Slovakian 28th seed Daniela Hantuchova and is still seeking her maiden Grand Slam title.
Wozniacki followed world number two Kim Clijsters out of claycourt Grand Slam as the top two seeds failed to advance past the third round at Roland Garros for the first time since 1971.
The Dane looked completely out of sorts under threatening skies on Court Suzanne Lenglen, falling 6-1, 4-0 behind in less than an hour.
Heading for an embarrassingly one-sided loss, Wozniacki broke back but Hantuchova ended her opponent's ordeal after 73 minutes.
Wozniacki, whose best Grand Slam performance was reaching the US Open final in 2009, left the court without looking at the crowd, her eyes staring at the clay.
Australian Stosur, last year's runner-up, could not locate her usual high-kicking serve and punishing forehand as she suffered a 6-4, 1-6, 6-3 defeat by Argentine world number 51 Gisela Dulko.
Defending champion Francesca Schiavone also started slowly but the Italian fifth seed fought back against Chinese Peng Shuai who was forced to quit after feeling dizzy while trailing 6-3, 1-2.
Schiavone will take on former world number one Jelena Jankovic after the Serb ignored Bethanie Mattek-Sands's painted face and thrashed the American 6-2, 6-2.
World number three Federer continued his smooth progress through the tournament in the shadow of Novak Djokovic and Rafa Nadal, thrashing Serbian 29th seed Janko Tipsarevic 6-1, 6-4, 6-3.
Ferrer demolished Ukraine's Sergiy Stakhovsky 6-1, 6-1, 6-3 and the Spanish seventh seed, who has not dropped a set in three matches, will next face France's Gael Monfils after the ninth seed eased past Belgian Steve Darcis 6-3, 6-4, 7-5.
Local favourite Marion Bartoli beat German prospect Julia Goerges after dropping the first set for the third time in a row and 2009 champion Svetlana Kuztnetsova continued her fine run with a 6-0, 6-4 thrashing of Canada's Rebecca Marino.
Federer was on and off court in a flash on Friday in his latest attempt to sneak up on the French Open field and catch them unawares with his almost forgotten brilliance.
Serbian 29th seed Janko Tipsarevic was the victim, ripped apart in exactly 90 minutes as a near flawless Federer again showed he cannot be discounted for the title despite his patchy record on clay.
Much of the focus in Paris has been on stuttering champion Nadal and red-hot Djokovic but 2009 winner Federer is lurking in the Roland Garros shadows and ready to pounce.
His choice of a red shirt this week almost makes him merge in with the red clay of the court but the third seed cannot go through the draw unnoticed any longer given he looks in better form than anyone except Djokovic. “Expectations are sky high for Novak and Rafa as defending champion. That leaves me out of a pressure situation and that's no bad thing for me,” a very relaxed Federer told a news conference.
“Overall it was a really good match for me and I'm happy to have another early finish.”
The record 16-times Grand Slam champion was especially impressive at the net, winning five out of five exchanges in the first set when he came forward.
The only break point offered in the second set was quickly gobbled up by Federer, who waited patiently for his chance in the third as he looks increasingly comfortable on his least favoured surface.
“I think my game is good enough to win here, sure, otherwise I wouldn't be here,” he said.
Indians sparkle
It turned out to be a good day for Indians with both Sania Mirza and Rohan Bopanna advancing to the third round of women’s and men’s doubles competiton respectively.
Seventh-seeded pair of Sania and Elena Vesnina of Russia defeated Kristina Barrois of Germany and Johanna Larsson of Sweden 7-6 (7-4), 6-3. They now await the winner of the match between two Spanish pairs -- 11th-seeded Maria Jose Martinez Sanchez and Anabel Medina Garrigues, and Lourdes Dominguez Lino and Laura Pous-Tio.
In the men’s doubles category, Bopanna and Pakistan’s Aisam-Ul-Haq Qureshi, seeded fifth, fought back from a set down for a 6-7 (4-7), 6-3, 6-4 win over Maximo Gonzalez of Argentina and Japan’s Kei Nishikori.
They next play Andrey Golubev of Kazakhstan and Denis Istomin of Uzbekistan.
Results (second round, prefix denotes seeding): Men’s singles: 14-Stanislas Wawrinka (Sui) bt 17-Jo-Wilfried Tsonga (Fra) 4-6, 6-7 (3-7), 7-6 (7-5), 6-2, 6-3; 13-Richard Gasquet (Fra) bt 23-Thomaz Bellucci (Bra) 6-2, 6-3, 3-6, 6-3; 9-Gael Monfils (Fra) bt Steve Darcis (Bel) 6-3, 6-4, 7-5; Albert Montanes (Esp) bt 12-Mikhail Youzhny (Rus) 6-1, 7-6 (7-0), 6-1; Fabio Fognini (Ita) bt 30-Guillermo Garcia-Lopez (Esp) 4-6, 6-3, 6-3, 6-1; 3-Roger Federer (Sui) bt 29-Janko Tipsarevic (Srb) 6-1, 6-4, 6-3; 7-David Ferrer (Esp) bt 31-Sergiy Stakhovsky (Ukr) 6-1, 6-1, 6-3.
Women’s singles: 14-Anastasia Pavlyuchenkova (Rus) bt Nuria Llagostera Vives (Esp) 3-6, 6-3, 6-3; 3-Vera Zvonareva (Rus) bt Anastasia Rodionova (Aus) 6-2, 6-3; 28-Daniela Hantuchova (Svk) bt 1-Caroline Wozniacki (Den) 6-1, 6-3; 11-Marion Bartoli (Fra) bt 17-Julia Goerges (Ger) 3-6, 6-2, 6-4; 13-Svetlana Kuznetsova (Rus) bt Rebecca Marino (Can) 6-0, 6-4; 10-Jelena Jankovic (Srb) bt Bethanie Mattek-Sands (US) 6-2, 6-2; 5-Francesca Schiavone (Ita) bt 29-Peng Shuai (Chn) 6-3, 1-2 (retd).
