Federer cruised past Leonardo Mayer, while Nadal handled Juan Ignacio Londero without too many issues.
In the women's draw, Johanna Konta beat Donna Vekic in straight sets. Garbine Muguruza and Sloane Stephens will battle it out in arguably the day's marquee contest later on Sunday.
Here are select results from Roland Garros' early Sunday action:
(3) Roger Federer bt. Leonardo Mayer: 6-2, 6-3, 6-3
(2) Rafael Nadal bt. Juan Ignacio Londero: 6-2, 6-3, 6-3
(26) Johanna Konta bt. (23) Donna Vekic: 6-2, 6-4
Marketa Vondrousova bt. (12) Anastasija Sevastova: 6-2, 6-0
For the full results, visit the event's official website.
Federer became the first man to contest 400 Grand Slam matches earlier this week and added yet another record with his easy win on Sunday:
The 37-year-old has barely been challenged so far this tournament, spending little time on court against overmatched opponents.
It was more of the same Sunday, with the final point illustrating the Swiss star's dominance:
Mayer had never made it to the fourth round at the French Open, and his struggles on the clay showed. He couldn't keep pace in the rallies and allowed Federer to step into the court time and time again, with disastrous results.
Federer's first real challenge awaits in the quarter-finals, where he'll face the winner of the match between Stanislas Wawrinka and Stefanos Tsitsipas. The latter knocked him out of the Australian Open earlier this year.
Londero didn't give Nadal significantly more trouble, although he flashed his ability on his favoured clay surface in the final set. But in the bulk of the rallies, he had no answers for the Spaniard's brilliance:
Nadal's next opponent will be the winner of the match between Kei Nishikori and Benoit Paire.
In the women's draw, Konta used efficient tennis to force her way past Vekic and into the quarter-finals. No British women's player had done so in over 30 years:
The 28-year-old has been steadily building up her form after a poor 2018 season, peaking at the Italian Open, where she made it to the final before losing to Karolina Pliskova. She'll face Stephens or Muguruza next.