Reigning champion Djokovic and 13-time winner Nadal are on course to meet in the quarter-finals, with the Spaniard seeded outside the top four at Roland Garros for just the second time.
World number one Djokovic strolled to a 6-3, 6-3, 6-2 win over Slovenia’s Aljaz Bedene and Nadal eased past Dutch 26th seed Botic van de Zandschulp 6-3, 6-2, 6-4.
“I’m always very motivated when I get on the court, with the desire to produce my best level each time. It’s not always possible to do it, but today it was very good,” said Djokovic.
The 35-year-old Serb is aiming to become the oldest men’s singles champion in Paris in the Open era as he chases a record-equalling 21st Grand Slam title.
Next up for Djokovic, who was also French Open champion in 2016, is a match-up with Argentina’s Diego Schwartzman, the 15th seed.
Nadal, the 21-time major champion, improved his record at Roland Garros to 108-3 after seeing off 2021 US Open quarter-finalist Van de Zandschulp.
He has now reached at least the fourth round in 17 of 18 visits to Roland Garros, with the exception of 2016 when he withdrew in the third round with a wrist injury.
“I think I played a good match against a good player. I’m very happy to win,” said Nadal.
The Spaniard had a break point for 5-0 in the third set, but Van de Zandschulp refused to roll over, winning
four of the next five games before Nadal put away his second match point, having saved a break point in between the two.
“You always feel a little bit the nerves to finish the match, so I’m happy to be through in straight sets,” said Nadal, who plays Canadian ninth seed Felix Auger-Aliassime for a place in the last eight.
“I think it was my best match of the tournament so far for two-and-a-half sets, so I’m very happy with that.”
– Anisimova, Gauff move on –
Amanda Anisimova, the 27th seed and a 2019 semi-finalist, advanced to the last 16 as injury-plagued Karolina Muchova retired down 6-7 (7/9), 6-2, 3-0 after falling and twisting her ankle midway through the second set.
Last year’s US Open runner-up Leylah Fernandez beat Olympic champion Belinda Bencic of Switzerland 7-5, 3-6, 7-5, while Aliaksandra Sasnovich defeated three-time Grand Slam winner Angelique Kerber 6-4, 7-6 (7/5).
Coco Gauff, the youngest player left in the French Open, made the last 16 with a straight-sets win over Kaia Kanepi, the oldest woman in the tournament at 36.
After saving a match point in a thrilling five-setter against countryman Albert Ramos-Vinolas, Spanish teenage star Alcaraz goes up against Sebastian Korda, the US 27th seed who won their meeting in Monte Carlo last month.
“I believe in myself, and of course I work hard every day,” said the 19-year-old Alcaraz.
“You have to have a good goal, good dreams. Of course trying to follow your dream. Work hard every day. I think that’s the secret.
“I’m still young, but I would say pretty experienced player now. I feel comfortable playing on the big stadium, big matches, playing in a Grand Slam. As I said, physically I’m strong. Mentally I’m strong, as well.”
Alexander Zverev, the third seed and 2021 semi-finalist, was also staring at defeat in the second round against Sebastian Baez, saving a match point on serve at 4-5 in the final set after fighting back from two sets down.
The German Olympic champion meets Brandon Nakashima of the US who is enjoying his best Grand Slam run on his Roland Garros main-draw debut.
It is the first time since Wimbledon in 2011 that all top 12 men’s seeds have reached the third round at a major.