Defending champion Federer produced a near-identical performance to his opening two wins to ease past Julian Reister 6-4 6-0 6-4 and become the first man to reach the fourth round.
"With my own form, I'm very happy," said Federer, who will play Stanislas Wawrinka after the 20th seed beat Fabio Fognini 6-3 6-4 6-1.
"I'm getting very few breaks, and that's obviously always a good thing looking ahead."
Four-time champion Nadal made short work of Argentinian Horacio Zeballas in a second-round match postponed from Thursday due to the rain.
His 6-2 6-2 6-3 success was just as comfortable as his opening victory and set up an intriguing third-round meeting with 28th seed Lleyton Hewitt.
"It's always important to play a little bit better every day," said Nadal.
Hewitt needed five sets to beat Denis Istomin 1-6 6-3 6-4 2-6 6-2 in a topsy-turvy affair, but third seed Novak Djokovic had few problems dispatching Kei Nishikori 6-1 6-4 6-4.
He will face Victor Hanescu (31), who beat Yuri Schukin.
Following Federer into the last 16 were last year's runner-up Robin Soderling, who beat Albert Montanes 6-4 5-7 6-2 6-3 and Jo-Wilfried Tsonga (8), who got past Thiemo De Bakker 6-7 (6/8) 7-6 (7/4) 6-3
In the women's draw, Svetlana Kuznetsova's defence of her French Open title ended last night when she was dumped out of Roland Garros in round three by Maria Kirilenko.
The sixth seed repelled two match points from her Russian opponent but Kirilenko made no mistake with her third to wrap up a 6-3 2-6 6-4 victory.
Justine Henin and Maria Sharapova will today meet for the first time since the former came out of retirement.
Sharapova, converted a one-set overnight lead into 6-3 6-3 success over Kirsten Flipkens, with Henin, seeded 22, polishing off Klara Zakopalova 6-3 6-3.
Top seed Serena Williams beat Julia Goerges 6-1 6-1 in just 55 minutes.