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.
Three-time champion Williams made the fourth round with a ruthless 6-3, 6-4 romp past German 11th seed Julia Goerges.
The 36-year-old American, three times a victor in Paris, swept aside the German 11th seed 6-3 6-4 in one hour and 15 minutes and will face Sharapova in a much-anticipated fourth-round clash on Monday.
Williams beat 17-seed Ashleigh Barty in the round of 64 on Thursday and defeated Kristyna Pliskova in the round of 128 on Tuesday at Rolad Garros.
But the head-to-head history is overwhelmingly in Williams' favor: She has won 19 of 21 meetings, including 18 in a row.
"Any time you play against Serena you know what you're up against", Sharapova said.
"I think this is just one of her best surfaces, and she always does really, really well here".
"I'm just really trying to get my bearings and trying to feel out where I am and see where I can go".
Serena Williams wasted little time ramping up her rivalry with Maria Sharapova after setting up a French Open fourth-round meeting with her old foe. However, if they have one shared interest it is their edgy relationship with the media and, in recent months, they have launched their own approved responses: Sharapova in a documentary put out by her agent IMG as well as a sugary book Unstoppable: My Life So Far; and Williams in a five-part documentary being shown on Eurosport.
"It's really special to be here again", said Williams.
Russian Federation gifts North Korea's Kim Jong-un a ‘box for secrets’
Kelly meeting him at the ceremonial diplomatic entrance on the South Lawn in full view of television cameras and photographers. North Korea's nuclear weapons programme has made significant advances in recent years and poses a threat to the United States.
"I'm concerned how that's going to work out for me, because normally in Grand Slams I do spend a lot of time at the site".
Sharapova did not want to delve too much into their bitter past on Saturday and instead simply concentrated on the match ahead by saying: "There is a lot of things in her game that she's done much better than I have".
"But I believe I can hold a trophy not only here, I believe I can do it in every tournament I play".
"She's probably a favorite in this match", said Williams.
Meanwhile, adding even more spice to Monday's duel in the dust at Court Philippe Chatrier is Williams's assertion that Sharapova is nearly obsessed by the American who is named more than 100 times in "Unstoppable".
Former champion Garbine Muguruza reached the last 16 with a comfortable 6-0, 6-2 win over Australia's Sam Stosur.
There is still a ways to go, but its moving in the right direction, said Williams, who made only three unforced errors in the first set, 12 in all.
"I will look forward to doing that if she wins this one".
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.
The American was also asked whether her experience of being at a Grand Slam had changed since becoming a mother.
I´m working on that (smiling).´ It´s striking to hear you say that your self is coming out, that Serena is coming out.