French Open 2021 Results: Winners, Scores, Stats from Thursday's Singles Bracket

The reigning champions at Roland Garros have not dropped a set through two rounds.

Rafael Nadal and Iga Swiatek cruised into the third round with victories on Thursday.

The women's titleholder has been the more dominant of the 2020 singles champions, after outscoring her two opponents 25-7 through four sets. 

Nadal faced some fight from Richard Gasquet in Thursday's night match on Court Philippe-Chatrier, but the Frenchman did not do enough to seriously threaten the Spaniard's title hopes. 

Last year's runners-up in Paris also breezed into the third round, with Novak Djokovic and Sofia Kenin picking up straight-set victories. 

Not every seeded player had such an easy day on the clay. Gael Monfils, Alex De Minaur, Aslan Karatsev, Nikoloz Basilashvili and Taylor Fritz were upset in the men's draw, while America's Sloane Stephens knocked out ninth-seeded woman Karolina Pliskova. 

Thursday French Open Results

Men's Singles

No. 1 Novak Djokovic def. Pablo Cuevas, 6-3, 6-2, 6-4

No. 3 Rafael Nadal def. Richard Gasquet, 6-2, 7-5, 6-2

No. 8 Roger Federer def. Marin Cilic, 6-2, 2-6, 7-6, (7-4), 6-2

No. 9 Matteo Berretini def. Federico Coria, 6-3, 6-3, 6-2

No. 10 Diego Schwartzman def. Aljaz Bedene, 6-4, 6-2, 6-4

Mikael Ymer def. No. 14 Gael Monfils, 6-0, 2-6, 6-4, 6-3

No. 18 Jannik Sinner def. Gianluca Mager, 6-1, 7-5, 3-6, 6-3

Marco Cecchinato def. No. 21 Alex De Minaur, 6-4, 6-1, 3-6, 6-1

Philipp Kohlschriber def. No. 24 Aslan Karatsev, 6-3, 7-6 (7-4), 4-6, 6-1

Carlos Alcaraz def. No. 28 Nikoloz Basiliashvili, 6-4, 6-2, 6-4

Dominik Koepfer def. No. 30 Taylor Fritz, 6-3, 6-2, 3-6, 6-4

We are one round closer to seeing two of the "Big Three" in men's singles tennis square off. 

Nadal, Djokovic and Roger Federer all advanced to the third round on Thursday, and the Swiss star was the only member of the group to drop a set. 

Federer also faced the toughest opponent in Marin Cilic, who is one of the few previous major champions on the men's circuit outside of the Big Three.

Cilic controlled the second set by winning two of his five break points and fending off all four of the break-point opportunities created by the No. 8 seed. 

Federer battled through a third-set tiebreak to regain the edge in the match and then finished off the Croatian with relative ease in the fourth set. 

The 39-year-old won two of his three fourth-set breaks, did not allow Cilic a chance to break serve and won nine of the 21 receiving points on his opponent's serve. 

Nadal appeared to be on a fast path to the third round after he put up a 6-0 first-set win over Gasquet. The Frenchman put up more of a fight in the second and third sets, but he still could not come close to matching the Spaniard's quality. Nadal is now 17-0 all-time versus Gasquet. 

Nadal sits on the lighter side in the top half of the men's bracket. No. 10 Diego Schwartzman and No. 18 Jannik Sinner are the only two seeds left in that section. 

Monfils, Karatsev and Basilashvili were all ousted from the those two portions, with the most stunning loss coming for Basilashvili.

Eighteen-year-old Carlos Alcaraz swept the No. 28 seed and could be a surprise quarterfinalist if he gets past Schwartzman in a potential fourth-round match. 

Federer and Djokovic will have to go through a crop of young Italian players to face off in the final eight. Marco Cecchinato, Lorenzo Musetti and No. 9 seed Matteo Berrettini are still alive in the top two portions of the draw. 

Women's Singles

Magda Linette def. No. 1 Ashleigh Barty, 6-1, 2-2 (retired) 

No. 4 Sofia Kenin def. Hailey Baptiste, 7-5, 6-3

No. 5 Elina Svitolina def. Ann Li, 6-0, 6-4

No. 8 Iga Swiatek def. Rebecca Peterson, 6-1, 6-1

Sloane Stephens def. No. 9 Karolina Pliskova, 7-5, 6-1

No. 13 Jennifer Brady def. Fiona Ferro, 6-4, 2-6, 7-5

No. 14 Elise Mertens def. Zarina Diyas, 4-6, 6-2, 6-4

No. 17 Maria Sakkari def. Jasmine Paolini, 6-2, 6-3

No. 18 Karolina Muchova def. Varvara Lepchenko, 6-3, 6-4

No. 24 Coco Gauff def. Wang Qiang, 6-3, 7-6 (7-1)

No. 25 Ons Jabeur def. Astra Sharma, 6-2, 6-4

No. 28 Jessica Pegula def. Tereza Martincova, 6-3, 6-3

No. 30 Anett Kontaveit def. Kristian Mladenovic, 6-2, 6-0

Barbora Krejicova def. No. 32 Ekaterina Alexandrova, 6-2, 6-3

Swiatek should be viewed as the favorite to win the women's title after turning in another dominant performance and top seed Ashleigh Barty being forced to retire from the tournament.

Barty made it through the first set and four games in the second against Magda Linette before a hip injury saw her call an end to her chance to win two French Open titles in three years. 

The Australian expressed her disappointment to reporters after the match:

"It's heartbreaking. We have had such a brilliant clay court season, and to kind of get a little bit unlucky with timing more than anything, to have something kind of acute happen over the weekend and just kind of run out of time against the clock is disappointing. It won't take away the brilliant three months that we have had, as much as it hurts right now."

Swiatek still has to navigate a portion of the bracket that is littered with seeded players, but she has been the most dominant of the top-tier stars through the opening rounds. 

WTA Insider highlighted just how in control the 20-year-old has been at Roland Garros in her first major title defense: 

Swiatek will face No. 30 seed Anett Kontaveit in the third round, and an unseeded opponent will await in the fourth round. 

At least two American women will qualify for the final 16 out of the top half. Coco Gauff will play Jennifer Brady in the third round, while Sofia Kenin meets Jessica Pegula. 

The victories by those players were overshadowed by Stephens' straight-sets upset of Pliskova, which moved her head-to-head record in the series to 4-1. 

Stephens finished off the victory in emphatic fashion by winning three of seven break points created and taking 16 of 28 receiving points on Pliskova's serve. 

Next up for the 28-year-old is a meeting with No. 18 Karolina Muchova. If she gets past that match, she could take on No. 5 seed Elina Svitolina in a bid to reach the final eight. 

Follow Joe on Twitter, @JTansey90.

Statistics obtained from RolandGarros.com.