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They had shared that record with Budge Patty but moved above the American with two more dominant displays, although 11-time champion Nadal did drop his first set of the tournament.
Nadal pulverised the unfortunate David Goffin into the Court Philippe Chatrier dust for two formidable sets but was made to sweat buckets in the soaring temperatures as 'Le Goff' dug in.
The Mallorcan second seed was never in serious trouble, however, and came through 6-1 6-3 4-6 6-3 to set up a clash with Argentina's 78th-ranked Juan Ignacio Londero.
"The level that I kept during the first 45 minutes, you can't really maintain that," Nadal said. "It was almost the top level, the highest level I could play."
The 37-year-old Swiss duly dispatched the youngster although he was pushed to a tiebreak in the third set on his way to becoming the oldest player to reach the fourth round since Nicola Pietrangeli in 1972 with a 6-3 6-1 7-6(8) victory.
"Very pleased how I'm feeling and how I'm playing, and still trying to stay true to playing freely and with nothing to lose," Federer, trying to repeat his 2009 title run having missed the last three French Opens, told reporters.
Like Nadal, he will also face an Argentine next in the form of Leonardo Mayer, who knocked out French veteran Nicolas Mahut.
Karolina Pliskova became the highest seed to fall so far when the Czech second seed was well-beaten, 6-3 6-3, by Croatia's Petra Martic in the day's opener on Court Philippe Chatrier, a match played in front of hundreds of empty seats.
Former champion Garbine Muguruza continued to impress in the women's draw as she overpowered ninth seed Elina Svitolina 6-3 6-3 and set up a clash with last year's runner-up Sloane Stephens who needed three sets to beat Slovenia's Polona Hercog.
Britain's sole remaining singles player Johanna Konta needed less than an hour to thrash Viktoria Kuzmova 6-2 6-1.
Day six saw two marathons.
Latvia's Anastasija Sevastova beat Elise Mertens 6-7(3) 6-4 11-9 in three hours 18 minutes, the longest match in the women's tournament so far, to set up a meeting with fast-rising Czech teenager Marketa Vondrousova.
In the men's draw seventh seed Kei Nishikori needed four hours 26 minutes to scrape past Serbian Laslo Djere.
Frenchman Benoit Paire kept the home flame burning as he reached the last 16 for the first time when opponent Pablo Carreno Busta retired with an injury.
Stan Wawrinka, the 2015 champion, was two sets up on Grigor Dimitrov when play was suspended for the night while Stefanos Tsitsipas was two games from victory over Filip Krajinovic when play was suspended at nearly 10pm local time.