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Spanish third seed Nadal, chasing an unprecedented eighth Paris title, saw off Slovakia's Martin Klizan 4-6, 6-3, 6-3, 6-3 to record his 54th win in 55 matches at the tournament.
For the second round in succession, the 26-year-old dropped the first set as he struggled in the cold, heavy conditions where the temperature just nudged over the 12-degree mark.
He then launched a blistering attack on tournament chiefs who he described as a "joke" and claimed he was being treated unfairly.
Nadal's match had been held over from Thursday after torrential rain swamped Paris.
He had been placed third on the Court Suzanne Lenglan schedule, following one men's match and a women's singles.
His third round opponent, Fabio Fognini, meanwhile, had been scheduled second on Court Three to follow just one women's singles match which took only an
hour to complete.
"The schedule was wrong, it was a bad decision," said Nadal.
Nadal was further incensed when he was told that Fognini had been given an earlier start time because he and opponent Lukas Rosol had doubles to play later together in the day.
"Today I was playing three hours while my opponent was in the locker room watching TV," said Nadal.
"I cannot play third when my opponent has played second. The excuse they gave me was that they had to play doubles, but that's a joke. In that case I should sign up for doubles. Sorry, but you can play doubles next week."
With third seed Nadal having to play his third round match on Saturday, second seed Federer had already ensured his place in the last 16.
His 6-3, 6-4, 7-5 win over France's 30th seed Julien Benneteau, who was restricted by a leg injury, marked his best start to the tournament.
As well as racking up his 57th win -- just one behind the record of 58 held by Guillermo Vilas and Nicola Pietrangeli -- the 31-year-old has also made the fourth round in record time.
He has dropped just 23 games in three rounds compared to 24 in 2007 and 27 in 2010.
Federer, the 2009 champion, next faces either Sam Querrey of the United States or Gilles Simon of France for a quarter-final place.
The 17-time major winner said that Nadal had just been unlucky with the scheduling.
"I understand the frustration, but it's complicated. Fifty percent of players couldn't complete their matches on Thursday," said Federer.
"It wasn't done on purpose. Either you are lucky or you are not."
Spanish fourth seed David Ferrer, who made the semi-finals in 2012, continued his low-key run.
Ferrer beat compatriot Feliciano Lopez, 6-1, 7-5, 6-4 to set-up a fourth round clash against either Canadian 14th seed Milos Raonic or 23rd seed Kevin Anderson of South Africa.
Anderson is hoping to become the first South African in the last-16 since Wayne Ferreira in 1996.
Croatia's 10th seed Marin Cilic was the biggest name to fall, losing 7-6 (14/12), 6-4, 7-5 to Serbia's Viktor Troicki.
Troicki could face Jo-Wilfried Tsonga, regarded as France's best hope of a first men's champion since Yannick Noah in 1983, in the next round.
Sixth-seeded Tsonga was facing compatriot Jeremy Chardy for a place in the last 16.
In delayed second round matches, there were wins for French seventh seed Richard Gasquet, who made the last 32 for the third successive year with a 6-3, 6-3, 6-0 win over Polish qualifer Michal Przysiezny.
German 12th seed Tommy Haas ended the run of American qualifier Jack Sock, 7-6 (7/3), 6-2, 7-5.
Haas, playing in his 52nd Grand Slam event, is the first 35-year-old to reach the third round in Paris since Jonas Bjorkman in 2007.
Haas will face another American in the fourth round, 19th seed John Isner who needed five sets to beat compatriot Ryan Harrison, 5-7, 6-7 (7/9), 6-3, 6-1, 8-6.
There were also second round wins for Serbian eighth seed Janko Tipsarevic, Swiss ninth seed Stanislas Wawrinka, Poland's Jerzy Janowicz, the 21st seed, and Russian 29th seed Mikhail Youzhny.
