The Russian - seeded seventh for the tournament - has emerged as one of the favourites at Roland Garros with Serena Williams, Li Na and Agnieszka Radwanska all making an early exit from the competition.
Sharapova certainly set down a marker in Friday's third-round clash with Paula Ormaechea - the 2012 champion whitewashing the Argentinian in a 6-0 6-0 demolition.
Her reward is a clash with Australian Stosur, and a 13-2 head-to-head record suggests the 27-year-old can be confident of a place in the quarter-finals.
However, Sharapova, who defeated Stosur at the Madrid Open earlier this month, is taking nothing for granted after
"I think this is one of her (Stosur) favourite surfaces to play on and a lot of her successes come on clay," she said.
"Despite my record against her and my victory a few weeks ago, this is a new match. I'm sure she's ready for the match against me, and so will I.
"I look forward to that challenge. She has a great serve, she uses the court extremely well, moves well on it."
Sharapova's only scare against Ormaechea came when she faced break points before and after a small delay for rain.
But in truth it was a completely one-sided affair, and Sharapova was pleased with how the match panned out.
She added: "I started off a little bit nervous, and I came back and I think she had another two break points when we came back after the rain.
"It was great to win that game, obviously get the advantage, and follow through with that.
"I thought as the match went on I started playing better and better, and it was great to get that match the way that I did."