But Williams thinks the Russian, who beat her in the 2004 Wimbledon final, has a competitive edge.
By the time the second set was merely one game old, she had been broken twice in the match, each time at love, a rather surprising development for the owner of one of her sport's most unsafe serves. NYT tennis reporter Christopher Clarey writes: "Serena Williams's personal life and priorities have certainly changed in the past 16 months, but she was not going to bid adieu to the French Open without a fight".
Fognini joins compatriot Marco Cecchinato in the fourth round, the first time that more than one Italian has made the last 16 since 1976.
Williams, playing in her first major since the birth of her daughter Alexis Olympia last September, had not been at her intimidating best in her previous two matches at Roland Garros this week.
"If I wasn't playing tennis, I'd be pregnant right now - sorry, I'm one of those women", she said. Williams, the holder of 23 majors, has strung together an 18-match winning streak against the Russian dating back to 2005.
"But that side of the game, I feel, has improved in the last few months and I like the challenge of coming up against a really good server".
Czech Pliskova made the semi-finals here a year ago, and may fancy her chances against Sharapova, who had to fight hard to get past Richel Hogenkamp and Vekic in her first two matches.
"I think she hated me for seeing her at her lowest moment".
"I don't even know what material it is, it looks like neoprene".
"I lost the first set and just thought "you know what?"
'I feel like a warrior in it, like a warrior princess kind of, [a] queen from Wakanda, ' she went on to explain.
"In the first set she gave me a hell of a lot of cheapies, a lot of errors", said the 25-year-old Australian who had secured her highest ever seeding at a major in Paris.
Williams and Sharapova meet in the fourth round Monday at Roland Garros.
"I don't expect extremely long rallies against an opponent like that", said Sharapova.
She had some problems in her initial two outings in Paris, including in the second round, when she dropped the first set against 17th-seeded Ashleigh Barty before - as Williams herself put it - "Serena came out".
"It's a Wimbledon final, you know". 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.
The 31-year-old is next to face home favorite Gasquet, his old junior rival who Nadal has beaten 15 times in as many meetings in professional tennis.
Garbine Muguruza is also safely through to the fourth round after destroying Australia's Sam Stosur 6-0, 6-2 in one and three minutes.
Williams, though, did not linger about to track the disfigured ball's final destination as that shot had sealed her the set.