Nadal, who got a first-round bye, defeated Richard Gasquet 6-3, 6-4 to advance.
A day after celebrating his 36th birthday, Federer played the aggressive game that has propelled him to five titles, including two grand slams, this year, attacking the net and rocketing second serves.
IMAGES from the matches played on Day 4 of the Wimbledon Lawn Tennis Championships at All England Lawn Tennis and Croquet Club on Thursday
Images from Day 3 of the 2016 Australian Open in Melbourne, on Wednesday
A summary of sports events and persons who made news on Sunday
India's Leander Paes and his German partner Alexander Zverev went down to the Spanish duo of Feliciano Lopez and Marc Lopez in a men's doubles first round match to bow out of the Cincinnati Open.
Serena Williams and Marin Cilic both survived third round scares on Friday to keep their US Open title defences on track but there was no escape for Rafael Nadal with the twice-winner going down in a late night thriller.
Second seed Garbine Muguruza, bidding to add the Wimbledon crown to her French Open title, was sensationally beaten in the second round on Thursday by Slovakian qualifier Jana Cepelova 6-3, 6-2 in the shock of the tournament so far.
