Seven-time winner and second seed Federer eased to a 6-4, 6-2, 6-2 win over Sam Querrey of the United States, the world number 36 who has now lost all three times he has played the Swiss and has yet to win a set.
Federer fired 32 winners and hit just nine unforced errors in an 86-minute Centre Court stroll with Querrey able to carve out just one break point.
The Swiss will face Australia's Sam Groth for a place in the last 16.
“I'm very happy with the way I've played now in the first two matches,” said Federer, the runner-up to Novak Djokovic last year.
“I've had a good run so you don't want it to stop in the first or second round,” he said.
“I guess there's also a little bit of relief that I'm actually playing well at Wimbledon.”
Federer admitted he loves being Wimbledon's great entertainer after producing a candidate for shot of the tournament in his demolition of Querrey.
He added to his repertoire of magical Centre Court moments in the second set.
Sprinting along the baseline, the Swiss great slipped the racket between his legs to direct the ball over the head of the stranded Querrey with an outrageous lob.
The 33-year-old's audacious piece of skill brought gasps from the crowd and admiration from Querrey, who was so impressed he said he felt like walking around the net to 'high-five' his opponent.
Take a look at the shot:
Third seed Murray, the 2013 champion, was equally dominant, taking just one minute longer than Federer to reach the third round by seeing off Robin Haase, the world number 78 from the Netherlands, 6-1, 6-1, 6-4.
The Briton smashed 25 winners past Haase and goes on to face either experienced Italian Andreas Seppi or highly-rated 18-year-old Croatian Borna Coric.
“I started quickly and Robin was a little bit slower at the beginning and then he started to come back in it, he played better tennis,” said Murray, after his fourth win in five matches against his fellow 28-year-old.
Murray caused some amusement when he threw his wristband into the crowd where it hit the head of All England Club chairman Phillip Brook, who then handed it as a gift to Prince Charles' wife Camilla who was sitting next to him.
“Normally you see who catches it. Then the Duchess opened up her bag and my wristband was in there, so he obviously had given it to her,” said Murray.
Women's defending champion Petra Kvitova reached the third round with a 6-2, 6-0 win over Japan's Kurumi Nara in a Court One little-and-large tussle.
Second seed Kvitova will face either Serbian 26th seed Jelena Jankovic or Russia's Evgeniya Rodina for a place in the last 16.
The Czech fired 10 aces and 23 winners in her 58-minute win over the world number 57.
In the first round, she dropped just one game against Kiki Bertens, winning in 35 minutes.
“It was a good match from my side,” said 1.82-metre (six feet) tall Kvitova, who towered over the 1.55-metre (five feet, one inch) tall Nara, the smallest player in the world top 100.
Former world number one Caroline Wozniacki made the third round with a 6-1, 7-6 (8/6) win over Denisa Allertova, the world number 83 from the Czech Republic.
Wozniacki, who has never got beyond the last 16, next takes on Italian 31st seed Camila Giorgi.
German tenth seed Angelique Kerber was also a winner, seeing off Russia's Anastasia Pavlyuchenkova 7-5, 6-2 while 2012 runner-up Agnieszka Radwanska, the Polish 13th seed, defeated Australia's Ajla Tomljanovic 6-0, 6-2.
However, the women's draw opened up even further when Russian eighth seed Ekaterina Makarova, a quarterfinalist in 2014, went down 6-2, 7-5 to unseeded Magdalena Rybarikova of Slovakia.
Before this tournament, the world number 65 Rybarikova had never won a match at Wimbledon in seven years of trying.
Makarova joined third seed Simona Halep, seventh seed Ana Ivanovic and Carla Suarez Navarro, seeded nine, in failing to get beyond the second round.
Rybarikova goes on to face Belarus qualifier Olga Govortsova who put out French 25th seed Alize Cornet 7-6 (8/6), 2-6, 6-1. Cornet knocked Serena Williams out of Wimbledon last year.
German 18th seed Sabine Lisicki, the 2013 runner-up, fought back to defeat Christina McHale of the United States 2-6, 7-5, 6-1.
Lisicki next meets French Open semifinalist Timea Bacsinszky, the 15th seeded Swiss.