PARIS, France - Inspired upset bids had been a dime a dozen, but unlike many of the other top players, this one survived - Maria Sharapova fought off an in-form Sam Stosur at the French Open, coming within points of going out before turning the match around and cruising into the quarters.

Though Sharapova dominated her head-to-head with Stosur, the threat level was high - not only had Stosur already beaten another Top 10 player this tournament, Dominika Cibulkova, but this is arguably her best surface, and this was also the first time the two players squared off at a Grand Slam.

From early on it was clear Stosur was dialed in - from 2-3 she won four straight games to claim the first set, 6-3, and after going down an early break she got the second set back on serve, and up 4-3, she threatened to get another break by winning the first point of Sharapova's service game. And when it got to 30-all, Stosur was just six points away from the victory - another Parisian shocker in the cards?

But with her back against the wall the No.7-seeded Sharapova went into complete battle mode, firing her groundstrokes with her trademark power and champion's precision, reeling off nine games in a row to send the No.19-seeded Stosur out, 3-6, 6-4, 6-0. She blasted her 25th winner of the match - an inside out forehand - on match point, then let out a war cry that echoed across Court Suzanne Lenglen.

"I thought Sam played a really good first set. With that said, I had five break points and I didn't convert one of them," Sharapova said after the match. "Against a player who's a very good server and who uses her serve as a weapon to set up points out there, if you don't take advantage of those particular moments, she gains a lot of confidence from that and swings and just keeps serving well too.

"And it was unfortunate that I gave that break back in the second set, because I thought I had a good start, but overall I'm happy with the way I finished. I think that's the most important thing."

Sharapova was asked about the emotion and energy she displayed on the court during the third set.

"Why wouldn't there be?" she said. "I'm in a Grand Slam fourth round. I lost in the fourth round of the Australian Open. I lost the first set playing an opponent who's played a great tournament so far.

"There's no reason why I should be walking around with my head down."

Next up for Sharapova is Garbiñe Muguruza, who beat French wildcard Pauline Parmentier in the last match of the day, 6-4, 6-2, to move through to the first Grand Slam quarterfinal of her career.

Sharapova beat Muguruza in their only previous encounter, on the clay courts of Rome last year.

Another quarterfinal was set, with No.14 seed Carla Suárez Navarro beating Ajla Tomljanovic, 6-3, 6-3, and No.18 seed Eugenie Bouchard powering through No.8 seed Angelique Kerber, 6-1, 6-2.

Suárez Navarro beat Bouchard in their only previous meeting, on the grass of Wimbledon last year.

Read more about Bouchard's win here, Suárez Navarro's win here and Muguruza's win here.