Seven-times champion Federer looked solid on serve and made the most of his Bosnian opponent Damir Dzumhur’s frequent mistakes to prevail 6-1 6-3 6-3 on a sun-bathed Centre Court.
And it was a similar story for Nadal on Court One, where Brazil’s Thomaz Bellucci did test him a couple of times but was still unable to take a set off the Spaniard, who is looking for a third Wimbledon trophy and made it through 6-4 6-2 6-4.
Federer was on court earlier than expected after Petra Kvitova’s 35-minute demolition of Kiki Bertens, and his own three-set match last only just over an hour, meaning Andy Murray’s arrival for the third match on centre came almost two hours earlier than expected.
Dzumhur struggled badly on serve, throwing in eight double faults to help Federer’s cause further, with the Swiss superstar hitting 26 clean winners as he strolled through.
Five breaks of serve through the game were enough to see him through to a second round clash with big-serving American Sam Querrey. Federer will be seeking a 75th individual Wimbledon victory in that match.
Nadal needed more than two hours to join Federer in the second round, and he showed the odd sign of the struggles that have seen him close to dropping out of the world’s top 10.
He was broken a couple of times by clay-court specialist Bellucci but neither proved costly as he set up a clash with Germany’s Dustin Brown.
Nadal had some issues on serve, sending down five double faults and only one ace, but his groundstrokes, in the main, were fluent and often too powerful for Bellucci to deal with.
He took six of 12 chances to break serve and was particularly effective when he decided to come to the net, where he took advantage of his opponent’s reluctance to challenge him and won 17 of 19 points.