The Russian has not beaten her nemesis since 2004 - before even the birth of Twitter and YouTube.
It's hard to understate how poorly Williams played in that first set.
Williams once again appeared in her striking, all-black catsuit.
Williams was quick to break and move into a 3-1 lead as she showed no signs of fatigue from her second-round win over Ashleigh Barty, which went to three sets.
Sharapova looks determined to beat her opponents and get her first Roland Garros campaign in the past three years back on track, seeking a third title.
She added: 'Why would I want to do that, and be that?
Sam Stosur exits the French Open. "She's been playing. for over a year now". "So I'm just really trying to get my bearings and trying to feel out where I am and see where I can go. I don't come here saying, "You can't win against me".
The top-seeded Romanian has never lost to Petkovic, and four of her seven wins have been on clay.
She next plays seventh-seeded Caroline Garcia of France, who cruised past Romania's Irina-Camelia Begu 6-1, 6-3, earlier in the day.
Only 59 minutes lasted the sixth favorite to the exnúmero one of the world, in the Philippe Chatrier court, where hours before the Venezuelan-born Spaniard Garbiñe Muguruza had eliminated Australian Samantha Stosur, by crushing 6-0 and 6-2.
Two-time Wimbledon victor Petra Kvitova was a third-round casualty, the eighth seed going down in two tie-breaks to Anett Kontaveit.
Argentina´s Juan Martin del Potro serves the ball to Spain´s Albert Ramos-Vinolas during their men´s singles third round match.
The 12th seed Angelique Kerber of Germany reached the fourth round when she defeated No.18 Kiki Bertens of the Netherlands 7-6 (4), 7-6 (4).
"Goerges is a strong player but I played and I won".
Two-time Grand Slam victor Angelique Kerber is through to the fourth round after winning 7-6 (4), 7-6 (4) against No. 18 Kiki Bertens.
The two will square off in the round of 16 on Monday, their first meeting in roughly two-and-a-half years.
The American will meet 11th seed Julia Goerges in the last 32 after the German beat former French Open quarter-finalist Alison van Uytvanck of Belgium 7-5 7-6 (7-5).
Seventh-seed Caroline Garcia mixed 18 winners and 13 unforced errors in a one-sided 6-1 6-3 victory against Irina-Camelia Begu to maintain hopes of a first home champion since Mary Pierce in 2000.
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