Federer, the second seed, trounced Indian qualifier Somdev Devvarman, ranked 188 in the world, 6-2, 6-1, 6-1 and next faces France’s Julien Benneteau.
It was Federer’s most one-sided win in Paris since he beat Belgium’s Kristof Vliegen in the first round in 2004, also for the loss of just four games.
The Swiss great’s latest French Open victory took him to 56, just two behind the tournament record held jointly by Guillermo Vilas and Nicola Pietrangeli.
“It’s great that all the work is paying off and I hope to keep experiencing this as long as possible,” said the 2009 champion.
Women’s top seed Williams cruised to a 6-1, 6-2 win over French teenager Caroline Garcia, conceding just seven points on her serve.
The 31-year-old American, who will face Romania’s Sorana Cristea, the 26th seed, for a place in the last 16, has dropped just four games in two rounds.
“I felt I was doing well, being serious and getting the job done,” said Williams.
“I like the clay here, I like to slide.”
Her 26th consecutive win in 2013 is only nine behind the record of 35 set by sister Venus in 2000.
In stark contrast, Danish 10th seed Caroline Wozniacki, a former world number one, went down 7-6 (7/2), 6-3 to Serbian world number 47 Bojana Jovanovski, who had defeated her in Rome two weeks ago.
Wozniacki had only snapped a five-match losing streak in the first round in Paris when she beat Britain’s Laura Robson.
“It hasn’t been the best clay season this year,” she admitted.
“I guess it’s good that it’s the last tournament.”
Sixth-seeded Jo-Wilfried Tsonga, cruised past Finnish veteran Jarkko Nieminen, 7-6 (8/6), 6-4, 6-3 as he continues his campaign to become France’s first men’s champion in 30 years.
Tsonga, a quarter-finalist last year when he squandered four match points against Novak Djokovic, next faces compatriot Jeremy Chardy.
“I’m French, it’s in France, and of course there may be a bit more pressure, but for me it’s positive,” said Tsonga.
Compatriot Gael Monfils, a semi-finalist in 2008, won a thrilling contest against in-form but unpredictable Latvian Ernests Gulbis, 6-7 (5/7), 6-4, 7-6 (7/4), 6-2 and next faces Spanish veteran Tommy Robredo.
Wildcard Monfils was playing his 12th match in 17 days after reaching the final in Nice last weekend.
“I don’t think about fatigue, I just hope to be ready for my next match,” said the 26-year-old who hit 29 winners and 33 unforced errors.
Gulbis finished with 52 winners but an ugly 69 errors.
In a match played in a fine spirit, Monfils even whipped his mobile phone from his bag at the end of the third set to film the crowd giving him a standing ovation after he had recovered from squandering five set points in the ninth game.
Spanish men’s fourth seed David Ferrer, a semi-finalist in 2012, also made the third round, beating compatriot Albert Montanes, 6-2, 6-1, 6-3.
In the women’s event, double Australian Open champion Victoria Azarenka cruised into the second round.
Third-seeded Azarenka clinched a 6-1, 6-4 win over Elena Vesnina — her fifth win in five matches against the experienced Russian — and will next face German 19-year-old Annika Beck, the 2012 junior champion, for a place in the third round.
Roland Garros has been Azarenka’s least successful Grand Slam.
Having reached at least the semi-finals of the other three majors, the 23-year-old’s best run in Paris saw her make the last eight in 2009 and 2011.
But she was relatively untroubled on Wednesday against Vesnina, with whom she reached the final of the women’s doubles in 2009.
“It felt good to be on the court after getting cancelled yesterday,” said Azarenka in reference to Tuesday’s rain-hit schedule.
Polish fourth seed Agnieszka Radwanksa, who has never got beyond the fourth round, eased past Mallory Burdette of the United States 6-3, 6-2.
She had been scheduled to tackle her sister for a place in the last 16, but Urszula Radwanska, who put out Venus Williams in the first round, crashed out 6-3, 6-3 to German qualifier Dinah Pfizenmaier, the world number 127.
Former champions, Svetlana Kuznetsova and Ana Ivanovic also went into the third round.
Kuznetsova saw off Magdalena Rybarikova, 1-6, 6-2, 6-2 while Ivanovic beat Mathilde Johansson, 6-2, 6-2