However, the three-time champion insists Sharapova, who dropped just three games as she brushed aside Karolina Pliskova, is the favourite to progress to the quarter-finals. She was broken in the first game of the match but that was the only blip in the match.
Fabio Fognini is through to the fourth round, giving Italy two players among the last 16 men for the first time since 1976.
The three-time champion and former world No. 1, dressed again in her all-black catsuit, is playing her first Grand Slam since winning last year's Australian Open while two months pregnant. She was beaten by Caroline Wozniacki in the Madrid Open second round, before suffering an opening round loss to Maria Sharapova in Rome.
The rivalry between the 2 has been a bitter one since the Russian's shock victory over Williams as a 17-year-old at Wimbledon, but she admitted that the "numbers don't lie".
Serena Williams introduces baby daughter to the world Thu, September 14, 2017 Serena Williams - The world's number one female tennis player in pictures. I feel like I wasn't really too much wrong.
Sharapova is competing at Roland Garros for the first time since 2015, following her 15-month doping ban and failure to qualify previous year. "I've got try harder". "And I think that as long as it's moving in the right direction, I know I will get there".
Fifth seed Juan Martin Del Potro advanced with a 7-5, 6-4, 6-1 win over Albert Ramos Vinolas and Belgium's David Goffin eliminated Frenchman Gael Monfils 6-7 (6-8), 6-3, 4-6, 7-5, 6-3. "I'm going to be here, fighting my heart out".
While Sharapova elaborated that the two were not friends but they have motivated each other, which is "better than being friends", Williams went on to say that she had no negative feelings towards her.
What did Maria Sharapova write about Serena Williams in her book?
"I always look forward to coming out on the court and competing against the best player", the five-time grand slam victor said.
"I have been able to put myself in this position of playing better tennis".
Other women moving into the fourth round included 2016 champion Garbine Muguruza, two-time French Open finalist Simona Halep, two-time major-title victor Angelique Kerber and reigning US Open champion Sloane Stephens.
Halep, seeking to reach her third French Open title, takes on Belgian 16th seed Elise Mertens, who booked her place in the last-16 with a 6-3, 6-1 win over Australia's Daria Gavrilova. "You know the challenge that is upon you", she continued.
The 36-year-old champion also dealt with a myriad of complications during her pregnancy.
The Spaniard, victor in 2016 and seeded third, took just 62 minutes to see off Stosur, the 2011 US Open champ, 6-0 6-2. She played a final here.
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