Federer rolled to a 6-2, 6-3 victory over Denis Istomin in a 58-minute rout, winning 25 of his 26 first-serves.
The Swiss superstar now goes on to meet Croatia's Ivan Dodig, who notched a 6-4, 6-2 decision over France's Julien Benneteau.
Nadal, meanwhile, needed a first-set tiebreaker to dispatch unseeded American Ryan Harrison 7-6 (7-3), 6-2 in another second-round match.
The Spaniard's next opponent will be Argentina's Leonardo Mayer, who bested Belgium's Xavier Malisse 6-2, 3-6, 6-4 in a 1-hour, 51-minute affair.
The news wasn't as good for Spain's Ferrer, however, who was bounced by South African Kevin Anderson 3-6, 6-4, 6-3.
Other second-round winners Saturday included No. 6 Czech Tomas Berdych, 10th-seeded Richard Gasquet of France, fellow Frenchman and 13th seed Gilles Simon, No. 20 Andreas Seppi of Italy, 18th-seeded Swiss Stanislas Wawrinka and No. 24 Jerzy Janowicz of Poland.