The 27th-seeded Gasquet trailed 5-0 in the first set before winning the next three games and moving 30-0 ahead on Nadal's serve.
Rafael Nadal continued his bid for an 11th French Open title on Saturday by brushing aside home favourite Richard Gasquet to claim a 16th consecutive win over his childhood friend and reach the fourth round.
The last time Sharapova beat Williams was in 2004. He has to try things out and not get caught up in the comfortable, predictable trading from the back of the court as Nadal will simply pick him off. That was the last time Gasquet took a set off Nadal on his favorite surface. The top-ranked Spaniard next faces unseeded German Maximilian Marterer in their first career meeting.
Sharapova advanced Saturday with a similarly lopsided win hours earlier, beating 2016 U.S. Open runner-up Karolina Pliskova 6-2, 6-1. Williams has won the French Open three times, Sharapova twice. Cilic reached the final at Wimbledon past year and at the Australian Open in January. Gene and Sandy Mayer did it at Wimbledon in 1979, and Emilio and Javier Sanchez followed suit at the 1991 U.S. Open.
Anderson is into the fourth round in Paris for the fourth time; he's never made it past that stage. Waiting for Williams as she competes in a major tournament for the first time in 16 months - and since giving birth in September - will be a familiar foe, Maria Sharapova. The big-serving Croat next faces No. 18 Fabio Fognini, who beat Kyle Edmund 6-3 4-6 3-6 6-4 6-4.
#PARIS Rohan Bopanna and his French partner Edouard Roger-Vasselin shocked top seeded Marcelo Melo and Lukasz Kubot in straight sets to reach the men's doubles quarter-finals. Sloane Stephens advanced too, but the 10th-seeded American had a much more hard time beating Italy's Camila Giorgi 4-6 6-1 8-6.
Sharapova has won two of her five Grand Slam titles at Roland Garros and is now into the fourth round for the 12th time in 14 appearances at the clay-court major. Stephens will be squaring off against No. 25 Anett Kontaveit.
The Belgian appeared to exchange angry words with his opponent during one changeover after Monfils was given a time violation before running out 6-7 (6/8) 6-3 4-6 7-5 6-3 victor. Playing better and better.More news: Asus Zenbook Pro has a 'smartphone' screen for a touchpad
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Alexander Zverev already has played a pair of five-setters.
Third-seeded Garbine Muguruza of Spain has crushed Samantha Stosur 6-0, 6-2 to advance to the fourth round of the French Open.
The last time they played was at the 2016 Australian Open.
Muguruza faced no break points in winning the first set in 26 minutes. She won 12 consecutive points on her serve during one run.
In other men's third-round play, No. 8 David Goffin saved four match points in a 6-7 (6) 6-3 4-6 7-5 6-3 win against Gael Monfils.
The 2016 French Open champion cruised to a 6-0 first-set win over the 90th-ranked Stosur.
When clay-court machine Rafael Nadal faces his old friend Richard Gasquet, the 10-time Roland Garros champion usually gets a free ride. They are scheduled for the afternoon on Court Suzanne Lenglen.