Defending champion Nadal is chasing a remarkable 12th title at Roland Garros and had little issue getting the better of Juan Ignacio Londero 6-2, 6-3, 6-3. Federer was also in sparkling form, as he continued his immaculate record at the competition this year with a 6-2, 6-3, 6-3 win over Leonardo Mayer.
Meanwhile, Stanislas Wawrinka got the better of Stefanos Tsitsipas in a five-set epic that lasted over five hours.
In the women's draw, 19-year-old Marketa Vondrousova shocked 12th seed Anastasija Sevastova.
Here are the results from Sunday's play and a closer look at the best of the action from Roland Garros.
French Open - Sunday Results
(2) Rafael Nadal bt. Juan Ignacio Londero: 6-2, 6-3, 6-3
(3) Roger Federer bt. Leonardo Mayer: 6-2, 6-3, 6-3
(24) Stanislas Wawrinka bt. (6) Stefanos Tsitsipas: 7-6 (6), 5-7, 6-4, 3-6, 8-6
Marketa Vondrousova bt. (12) Anastasija Sevastova: 6-2, 6-0
(26) Johanna Konta bt. (23) Donna Vekic: 6-2, 6-4
(31) Petra Martic bt. Kaia Kanepi: 5-7, 6-2, 6-4
Having been a little below his usual stunning standards in the previous round against David Goffin, Nadal was back at it again Sunday.
The Spaniard was into his rhythm quickly, making it hard for Londero to establish any sort of momentum in the contest. The victory took his tally of wins at Roland Garros to an extraordinary number; here's the moment the match was wrapped up:
One of the only players in the draw who looks capable of stopping Nadal is Federer, as the veteran Swiss is performing brilliantly on his return to the French Open for the first time in four years.
Mayer had no answer to Federer's blend of finesse and ferocity on the clay, as the Swiss breezed into the next round. Tennis journalist Reem Abulleil noted how quickly the third seed has been dispatching his opponents in Paris:
The AFP Sport account broke down the numbers behind Federer's efforts at the French Open in previous years:
AFP Sport @AFP_Sport
Roger Federer reaches 12th Roland Garros quarter-final, beating Leonardo Mayer 6-2, 6-3, 6-3. + Record-equalling 54th Slam QF + Oldest man since 1991 in last-eight at major + Could face friend Wawrinka in repeat of 2015 QF + 'Stan beat me with his terrible shorts.' #RG19 https://t.co/ffsDZWe7mB
In the match of the day, Tsitsipas and Wawrinka slugged it out in a five-set epic. The latter twice went a set ahead, only to be pegged back by his young opponent; however, at the end of a tense decider, Wawrinka dug deep and was able to seal the victory with a stunning backhand winner down the line.
In the women's draw, the standout performance came from Vondrousova, as she continued her exceptional run at the competition.
The WTA Insider account reflected on what has been an exceptional few months for the youngster:
Her progression also continued a trend of teenage players thriving at the French Open this year:
There was also a win for Johanna Konta, as she comfortably came through her match with Donna Vekic. Having never previously won at Roland Garros before this year's edition, the Briton is now playing as well as any player in the draw.
In the women's bracket on Monday, defending champion Simona Halep will be in action against Iga Swiatek, while men's top seed Novak Djokovic is up against Jan-Lennard Struff.