Handling pressure is something Maria Sharapova has been doing all her career, even from before she turned professional, and the Russian is handling the tag of favourite for the French Open just as impressively.

Trailing Australian Sam Stosur by a set, Sharapova was struggling at 3-4 on serve before reeling off nine games to win 3-6, 6-4, 6-0 to take her place in the last eight.

The champion in 2012 and the runner-up to Serena Williams a year ago, Sharapova was quickly installed as favourite as soon as world No.1 Williams was beaten in round two and world No.2 Li Na joined her on the sidelines.

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Simona Halep, seeded four, who plays American Sloane Stephens in the fourth round today, is the highest remaining seed but seventh seed Sharapova is the one everyone has to beat.

"I felt like I'd had opportunities," Sharapova said of the first set. "I just didn't win them. That was the bottom line. You can talk about all this and that but when you don't make your opponent think a little bit out there it can be quite tricky. I was happy with the way I was able to change things around, I guess.

"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 for me."

With a 13-2 head-to-head record over Stosur, Sharapova must have gone into the match high on confidence.

But a former US Open champion and the runner-up here in 2011, Stosur, now working with Andy Murray's former coach, Miles Maclagan, played perfectly to take the first set. The Australian then got back on terms after an early break and had her chances only for Sharapova to get on a roll and roar to victory.

"I know it was an opportunity lost," Stosur said. "I thought I was there to win that match; definitely playing well enough to do so. I know that's an opportunity I'm not going to get again. But on the flip side, I know I had a good tournament. I played well here. Probably some of the best tennis I have played for quite a few months. It's something that I'm definitely very happy about, something I'm going to build on."

Sharapova could play Eugenie Bouchard, the Canadian rising up the rankings, in the semi-finals but first she must beat another upstart, Garbine Muguruza of Spain.

Muguruza took out world No.1 Serena Williams in round two and maintained her momentum last night with a 6-4, 6-2 win over France's Pauline Parmentier.

"I feel amazing," the 20-year-old Muguruza said. "I didn't expect this. It's a present."

Unusually for a Spaniard, Muguruza says she favours grass courts and her hard, flat groundstrokes would certainly be a good fit at Wimbledon. For now, though, she is focused on playing Sharapova and knows she can go for broke. "It's a tough match again but nothing to lose; everything to win," she said.

"Obviously people start having more expectations when you win such a match [as against Williams]. But with my team, we have tried to set this aside and to remain focused. I'm very happy so far. I'm enjoying this victory, and I will think about the next match afterwards."

Another Spaniard, the No.14 seed Carla Suarez Navarro, also won, seeing off Ajla Tomljanovic of Serbia 6-3, 6-3. Her reward is a match with 18th seed Bouchard, who upset No.8 seed Angelique Kerber 6-1, 6-2.