While Sharapova has spoken in the past of her struggles against Williams, who she has beaten only twice on the WTA Tour, she is in confident mood after a fine start to her campaign in Paris.
Sharapova is seeded for the first time at a Grand Slam since her suspension for using meldonium and is playing her first French Open since 2015 after being refused a wildcard by tournament organisers previous year.
Williams - playing in a grand slam for the first time since giving birth last September - triumphed 6-3 6-4 against German Julia Goerges after 75 minutes on court.
Williams then charged on to win the set and match 6-4, seemingly getting better with each match she plays.
If that topsy-turvy performance had given Goerges hope that she could finish off a job that Barty could not - it did not take long for reality to sink in.
With her return to tennis now at full speed, Williams sent a big statement to her rivals.
The pair's fierce rivalry has been dominated ever since by Williams, who has won the past 18 matches against Sharapova. Especially having a daughter, like, I feel like negativity is taught.More news: USA may open door to more temporary immigrant workers, Trump aide says
The two players met in the Paris final in 2013 and in the quarterfinal of the 2016 Australian Open, which was Sharapova's last match before a 15-month doping ban. I go extremely hard.
"Still, I believe you've got to distance yourself a little from the name of your opponent".
"Any time you play against Serena you know what you're up against", Sharapova said.
Top seed Simona Halep came through 7-5 6-0 against Andrea Petkovic and Caroline Garcia, the seventh seed, beat Irina-Camelia Begu 6-1 6-3. "So of course I wanted to read it [Unstoppable] and just see what was going on".
Sharapova famously hinted Williams was dating her coach, Patrick Mouratoglou, while in an open letter posted to Reddit a year ago, Williams wrote: "It has been said that that [sic] I use drugs". And she's playing really well, and I think this is really her best surface, so we'll see.
Some might be surprised by the way Sharapova eased past Pliskova but not the latter's compatriot Petra Kvitova, who saw her 13-match winning streak come to an end at the hands of 25-seeded Estonian Anett Kontaveit on Saturday.
"You know that the challenge is upon you". "I was, like, 'Oh, OK, I didn't expect to be reading a book about me - that wasn't necessarily true'". And if her comeback continues to progress as it has so far, the 36-year-old Williams has every chance to tie and break the record. 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.
Defending champion Rafael Nadal has advanced to the fourth round of the French Open with a 6-3, 6-2, 6-2 win against Richard Gasquet, improving to 16-0 against the Frenchman. Sharapova has won 10 of her last 12 matches on clay court.