The 13th seeded Indo-French combination went down 6-7, 2-6 to eighth seeds Nikola Mektic of Croatia and Austria's Alexander Peya in an hour and 32 minutes.
Their matchup provides a contrast in styles: Keys is a big hitter whose serves and forehands are the keys to her success; Stephens covers every inch of the court as well as anyone.
The former world number one Djokovic took two hours and 25 minutes to get into the last eight at Roland Garros for the 12th time on Sunday.
The 10th-seeded Stephens was a 6-2, 6-0 winner against No. 25 Anett Kontaveit of Estonia in 52 minutes, while No. 13 Keys beat No. 31 Mihaela Buzarnescu of Romania 6-1, 6-4 in 65 minutes.
Through 14 years and 21 matches, Serena Williams vs. Maria Sharapova has evolved into one of the most enduring and multi-faceted, if also lopsided, rivalries in women's sport.
Both Serena and Venus, who have won 14 Grand Slam doubles' titles, last won the French Open together way back in 1999.
Marco Cecchinato earned the right to face Djokovic for a spot in the semifinals at Roland Garros by eliminating the No. 8-seeded David Goffin 7-5, 4-6, 6-0, 6-3 on Sunday.
The head-to-head history is overwhelmingly in Williams' favour as the American has won 19 of 21 meetings against Sharapova, including 18 in a row.
Nadal is gaining momentum in his bid for a record-extending 11th title at Roland Garros, and Gasquet never looked remotely like stopping him.
It's the third time that Bopanna has reached quarterfinal stage at Roland Garros. He made it to the last-eight pairs in 2011 and 2016 also.
Top-ranked Simona Halep, third-seeded Garbine Muguruza and two-time champion Maria Sharapova all powered into the French Open's third round with straight-set victories on Thursday.
Bopanna and his French partner Roger-Vasselin began their Roland Garros campaign with a comfortable win over the American team of Taylor Fritz and Frances Tiafoe.
Returning to the place where he claimed the second of his three Grand Slam titles did not help Wawrinka shake off his poor form.
Chung, who had to retire in his semifinal against eventual champion Roger Federer at Melbourne Park in January because of severe blisters, said he had been carrying the ankle injury through the clay-court season.
Nadal is 79-2 for his career in the French Open, a .975 winning percentage and he is 104-2 in all best-of-five-set matches on clay.
Roland Garros director Guy Forget says that the total prize money will reach 39.197 million euros (USD 48 million), an increase of about 3 million euros from last year.
Jelena Ostapenko, ranked only 47th and just two days past her 20th birthday, became one of the most unlikely Grand Slam champions in tennis history.
20-year old Jelena Ostapenko's carefree approach has helped her to storm into her first Grand Slam final where she will be up against the 2014 French Open runner-up Simona Halep.
'Stan the Man' defeated world number one Andy Murray in a grueling five-setter to set a date against 'King of Clay' Rafael Nadal in the final of men's singles at French Open 2017.
37-year old Rohan Bopanna feels he has become more mature as a player and is playing the best tennis of his career right now. Bopanna won the mixed doubles French Open title with his Canadian partner Gabriela Dabrowski
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