Romania's Simona Halep, the fourth and highest seed remaining in the French Open, qualified for the quarter-finals for the first time on Monday when she overcame America's Sloane Stephens 6-4, 6-3.
The 22-year-old Halep can climb to third in the world if she reaches the final on Saturday where she can become the first Romanian to win the title since Virginia Ruzici in 1978.
"I'm really happy to reach the quarter-finals in Paris for the first time in my life," said Halep, who also reached the same stage at this year's Australian Open where she was beaten by Slovakian Dominika Cibulkova.
"I feel confident and I like the clay but I want to go further even if I know it's going to be very tough in the next round."
In Wednesday's second set of quarter-finals, she will have to overcome the challenge of Russia's 2009 French champion Svetlana Kuznetsova, who ousted 24th seed Lucie Safarova of the Czech Republic 6-3, 6-4.
Kuznetsova, who won her first Grand Slam at the US Open in 2004, is one of two former champions remaining in the draw alongside compatriot Maria Sharapova, the 2012 winner.
Sara Errani of Italy will face German Andrea Petkovic for a semi-final berth after both players came through tough fourth round matches.
Tenth seed and 2012 finalist Errani, needed 81 minutes to subdue former number one Jelena Jankovic in the first set before booking her last eight spot for the third straight year 7-6 (7/5), 6-2.
She was beaten in the semi-finals last year by eventual champion Serena Williams 6-0, 6-1.
Petkovic, who failed to negotiate qualifying in Paris last year when she came into the tournament ranked 136 in the world, also had difficulties before prevailing in three sets over Dutch qualifier Kiki Bertens.
The Bosnian-born Petkovic, who is now ranked 27 and had a personal high of nine in the world during her finest season in 2011, has overcome a series of injuries to equal her best showing at a Grand Slam thanks to a 1-6, 6-2, 7-5 victory.
It's her fourth appearance in the last eight of a major after reaching this stage in 2011 at Australia, Paris and the US Open.
"I was really relieved that I picked myself up after I was up 4-2 in the third and I started playing a little passively," said Petkovic.
"I wasn't going for my shots anymore and I was sort of hoping that she's gonna miss. She's too good for that. After going down 5-4 in the third, I just sort of told myself, Okay, listen, you have to play aggressive.
"You have to go for your shots, and nobody's going to give you the quarter-finals just because you're nice, so go gain it."
Petkovic admitted she knew little of Bertens before Monday's match.
"It was super tough, because I didn't know her at all. I just stalked her on YouTube yesterday the whole day, and I was already impressed," added the German.
Bertens, a former world number 41, was bidding to become the 10th qualifier to advance to the quarter-finals in Paris and equal the best result from a player not going straight into the main draw.
On Tuesday, Sharapova faces Spaniard Garbine Muguruza, who knocked out defending champion Serena Williams in the second round.
The day's second quarter-final sees Canada's Eugenie Bouchard targeting a second straight Grand Slam semi-final against Spanish 14th seed Carla Suarez-Navarro.
Bouchard reached the last four in Australia earlier this year where she lost to eventual champion Li Na of China.