Paris, France (SportsNetwork.com) - Serena Williams survived her fourth-round match against fellow American Sloane Stephens, while defending champion Maria Sharapova was not as fortunate Monday at the French Open.

The world No. 1 Williams struggled over the first two sets against Stephens before completing a comeback in 1-6, 7-5, 6-3 fashion at Court Chatrier.

Stephens broke Williams three times in the opening set, going surprisingly uncontested in the stanza, but the lethargic Williams broke Stephens on two occasions in the second to tighten things up.

The 22-year-old Stephens was one game away from the biggest win of her career at 5-4 in the second, but Williams won three straight games to right the ship on Day 9 of the fortnight.

The third set was tied up before Williams broke for a 3-2 lead and ultimately finished the match on Stephens' serve with a dipping cross-court backhand winner.

The 33-year-old Williams is now 4-1 lifetime versus Stephens, who shocked the powerful star in an Aussie Open quarterfinal two years ago.

Williams, who misfired for 43 unforced errors, has had to work hard to make progress this year and labeled her performance unprofessional after defeating Germany's Anna-Lena Friedsam in the second round last week.

She also dropped the first set in the third round against former No. 1 Victoria Azarenka.

The 19-time Grand Slam champion Williams owns two French Open titles (2002, 2013) and is the reigning Aussie and U.S. Open champ.

She's now a sizzling 29-1 this year and her quarterfinal opponent will be pesky Italian Sara Errani.

And there will be a new champion at the French this year after Sharapova was eliminated by Czech Lucie Safarova.

The 13th-seeded Safarova pulled off one of the biggest wins of her career with a 7-6 (7-3), 6-4 triumph over the two-time French winner in a match that was postponed on Sunday because of rain.

"I had a few small openings but I wasn't able to keep up my level. She was more consistent and aggressive, created the angles and that was the difference," said Sharapova, who had been battling a heavy cold since last week.

"It was a tough day at the office."

Safarova will play in the quarterfinals for the first time in 11 visits to Roland Garros. She had reached the fourth round twice, falling in the round of 16 in 2007 and again last year.

It will also be the Czech's third quarterfinal at a major championship since making her Grand Slam debut at the 2005 French Open. She lost to Nicole Vaidisova in the 2007 Australian Open quarters and beat Ekaterina Makarova at Wimbledon last year in the round of eight before losing to eventual champion Petra Kvitova in the semifinals.

The former world No. 1 Sharapova had beaten Safarova in four of their five previous meetings, including the last four, but the last three had gone the distance and Monday would prove to be too difficult of a challenge for the second-seeded Russian star.

After Safarova prevailed in the first-set tiebreak, she opened a 3-0 lead in the second set. Sharapova fought back to win the next three games, but could not hold serve at 4-5.

Safarova failed to convert her first match point with a forehand into the net, but followed with a forehand winner to end Sharapova's run of three straight French Open finals.

The five-time major champion Sharapova won the 2012 French title to complete a career Grand Slam, then lost to Williams in the 2013 final before winning the title again last year. She has now lost in the fourth round in four of her last six major championships, falling at this exact stage in 2014 at the Australian Open, Wimbledon and the U.S. Open.

The left-handed Safarova, who won her sixth career WTA title earlier this year in Doha, will next play 21st-seeded Spaniard Garbine Muguruza, who advanced to the French Open quarters for a second straight year with a 6-3, 6-4 victory over 28th-seeded Italian Flavia Pennetta.

"Here again, I have reached the quarterfinals. It's a great leap forward already. It's Roland Garros. There's a lot of pressure. So I'm very happy to have gone that far already," said the Venezuelan-born Muguruza.

Safarova-Muguruza will be part of Tuesday's schedule.

Both of the early matches on Monday had been scheduled for Sunday, but a nearly three-hour rain delay forced officials to push them back a day.

Also on Monday, the former French Open runner-up Errani, seeded 17th, cruised past German Julia Goerges 6-2, 6-2 to pull within two victories of reaching a second French Open final in four years, while Belgian Alison Van Uytvanck cruised past Romanian fellow non-seed Andreea Mitu, 6-1, 6-3. The gritty Italian Errani was the 2012 Roland Garros runner-up to Sharapova and has reached at least the quarters in Paris four years running.

The 21-year-old Van Uytvanck will appear in her first Grand Slam quarterfinal in her sixth major event. She was a first-round loser in four of her first five Slams.

In addition to Safarova versus Muguruza, another quarterfinal on Tuesday will pit seventh-seeded former world No. 1 Ana Ivanovic against 19th-seeded Ukrainian Elina Svitolina. The Serbian star Ivanovic reached back to-back French Open finals in 2007 and 2008, including her lone Grand Slam title here in '08.