Barty gave an out-of-sorts Williams a reality check as she won the first set Thursday, but the 36-year-old showed quality and spirit that has made her one of the greats by roaring back to win 3-6, 6-3, 6-4.
In her glittering career so far Williams has won 23 Grand Slam titles - one away from the record held by Australia's Margaret Court.
"She will not want to leave early because she loves Paris", Courier, victor in 1991 and 1992, said.
However, by highlighting that single word it summed up where Williams, the victor of 23 major titles, thinks her place is among the sporting greats.
Czech world number 70 Pliskova questioned the legality of the Williams outfit when she talked with Czech media after the first round match.
But Sharapova rediscovered her game in the nick of time to reel off half a dozen games for a 6-1 4-6 6-3 victory.
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Her comeback has been stop-start so far, and she dedicated her win on Tuesday to "all the moms out there who had a tough recovery from pregnancy".
"That's the reason I have success, because I go every day on court knowing that I can win, that I can lose, and that's the sport".
"Any time you get to play a champion like Serena, it's wonderful", Barty said in her postmatch interview in Paris. "And Serena came out", she said.
Williams also believes that fighting back from losing the first set will be beneficial in sharpening her game. "I definitely feel like it is an opportunity for me to inspire a whole different group of unbelievable women and kids".
Karolina Pliskova is coming off a three sets win over Lucie Šafářová that took 26 games to decide.
"I mean, I played well". I just respect the decisions of the other players.
Serena eventually closed out the match 3-6, 6-3, 6-4, in an hour and 46 minutes.
"Next up for Serena is 17th seed Ashleigh Barty. I don't want to limit myself".
"People would say I was born a guy, all because of my arms, or because I'm strong", she said.