Federer needed only 61 minutes to speed past Croatia's Ivan Dodig 6-3, 6-1, cruising into the round of 16.
He'll next face fellow Swiss and No. 18 seed Stanislaw Wawrinka, who bested Australian Lleyton Hewitt 6-4, 7-5.
Nadal, meanwhile, didn't even have to take to the court to advance into the fourth round. He was set to meet Leonardo Mayer on Day 5, but the Argentine pulled out of their scheduled third-round match with a back injury.
The Spanish superstar now goes on to face Latvian Ernests Gulbis, who rallied for a 5-7, 6-3, 6-4 victory over Italian Andreas Seppi.
Also Monday, sixth-seeded Czech Tomas Berdych needed only 68 minutes to dispatch No. 27 German Florian Mayer 6-4, 6-1; 13th-seeded Gilles Simon outlasted Frenchman Benoit Pare 3-6, 7-6 (7-5), 6-4; and No. 10 Richard Gasquet of France bested 24th-seeded Pole Jerzy Janowicz 6-1, 6-4.