Sharapova, who thrashed Karolina Pliskova in the third round, will face Williams for the 22nd time in the last 16 on Monday, after the American saw off Germany´s Julia Goerges 6-3, 6-4.
Having been banned for 15 months for violating the anti-doping rules, Sharapova is beginning to work her way back to the top, but is still ranked just 28 in the world. Breaks were the name of the game in the first set, as Sharapova clawed back to 4-4.
Argentinian fifth seed Juan Martin del Potro reached the French Open fourth round for the first time in six years by seeing off Albert Ramos-Vinolas on Saturday.
Sharapova is seeded for the first time at a Grand Slam since her suspension for using meldonium and is playing her firstFrench Open since 2015 after being refused a wildcard by tournament organisers past year. Barty took over a year away from the game of tennis also-but in her case, it was to pursue a professional cricket career.
There have been clashes over their private lives, while Sharapova claimed a year ago in her book that Serena "hates" her for hearing her cry after the 2004 Wimbledon final.
There is a great mutual respect between the pair, as both Sharapova and Williams have made successful ventures into business and fashion, but the 31-year-old insists that is only possible if they continue to star on the court. The match was hyped like a Grand Slam final, with the tournament played at Wimbledon.
Sharapova seems finally free of the injuries that have plagued her since returning from a 15-month doping ban in April previous year.
"Honestly, sometimes I think I still have to deal with it. I'm playing tougher opponents and I'm hanging in there", said Williams, whose trophy collection includes three Suzanne Lenglen Cups.
"I love how proud they are, I am planning to go over there, do not know if this year or next year, it is going to be fun!"
"I thought there would be a lot of reactions over the outfit", she said.
Williams hit just three winners in the opener while 22-year-old Barty could afford to bide her time, just two winners and four unforced errors.
Sharapova, the victor in Paris in 2012 and 2014, missed last year's edition after being denied a wild card following her return to the game from a doping exile, but had little trouble against sixth-seed Karolina Pliskova. I have been wearing trousers in general a lot when I play so I can keep, you know, the blood circulation going.
In other women's matches, world No. 1 Simona Halep advanced 7-5, 6-0 over Andrea Petkovic and Germany's Angelique Kerber went through 7-6 (7-4), 7-6 (7-4) over Kiki Bertens. Williams not only sprinted to the ball in time, she whipped a cross-court forehand passing victor to go up 3-1, then let out a loud yell and raised her fist.
Serena Williams is coming off a straight sets win over Julia Goerges that took 19 games to decide.
Spanish third seed Garbine Muguruza, the 2016 champion, was too strong for French No. 257 Fiona Ferro 6-4, 6-3. "I was, like, 'Oh, OK, I didn't expect to be reading a book about me - that wasn't necessarily true'".
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