Second seed Nadal is gunning for a third title at the All England Club, and the Spaniard began his quest on Tuesday by beating Martin Klizan for his 700th career victory.
However, Nadal did not have it all his own way as a shaky start saw him lose the first set before he rallied for a 4-6 6-3 6-3 6-3 victory on the famous grass courts.
An intriguing contest with Lukas Rosol now awaits in round two, after the Czech defeated Frenchman Benoit Paire.
Rosol famously sent Nadal packing in the second round at SW19 in 2012, and has the chance to repeat the shock when the two meet on Thursday.
Federer's quest for a record eighth Wimbledon title began in fine fashion as he steamrollered his way past Paolo Lorenzi in a 6-1 6-1 6-3 triumph, setting up a meeting with Gilles Muller, the conqueror of Julien Benneteau.
Fourth seed Federer, whose last slam title came at Wimbledon in 2012, was at his majestic best, while Lorenzi now has a woeful 0-13 record in the slams, the second worst in history.
Another Swiss star, Stanislas Wawrinka, was in dominant form as he reached the second round of Wimbledon for the first time since 2011.
The Australian Open champion was knocked out in the first round of last month's French Open, but there was to be no repeat failure as the fifth seed effortlessly defeated Joao Sousa 6-3 6-4 6-3.
Fellow seeds Milos Raonic, John Isner and Kei Nishikori all breezed through in straight sets, while Jo-Wilfried Tsonga's back-and-forth five-setter with Jurgen Melzer - which started on Monday - ended 6-1 3-6 3-6 6-2 6-4 in the Frenchman's favour.
Tsonga's compatriot Richard Gasquet also went the distance, the 13th seed defeating Australian James Duckworth, while Dusan Lajovic ousted 28th seed Guillermo Garcia-Lopez 7-6 (7-5) 6-2 3-6 3-6 6-3, the match marking the Serbian's first five-setter.
Big-hitting 15th seed Jerzy Janowicz, Julian Reister, and Yen-Hsun Lu also needed five sets to progress, but Jiri Vesely had a much easier task. He was leading 5-1 when his opponent Victor Estrella retired.
Ivo Karlovic, the 29th seed, was toppled in three sets by Frank Dancevic, while Gael Monfils, Feliciano Lopez, Lukasz Kubot, Santiago Giraldo, Ante Pavic, Jarkko Nieminen, Philipp Kohlschreiber, Mikhail Kukushkin and Adrian Mannarino were also straight-sets winners.
Elsewhere, there were wins in four sets for Sam Querrey, Nick Kyrgios, Jack Sock, Denis Istomin, Marcel Granollers, Simone Bolelli, Tommy Robredo, Denis Kudla and 2002 champion Lleyton Hewitt.