Top seed and world number one Murray downed Kazakh lucky loser Alexander Bublik 6-1, 6-4, 6-2, shrugging off two brief rain delays and showing little sign of the hip problem which had plagued him in the build-up.
"I have felt OK the last few days and the adrenaline you feel by playing a match numbs any pain you may have," said the British star after seeing off world number 134 Bublik who was making his grass court debut.
"Bublik is a bit of a character. He's a bit different from other players, tries different shots and the crowd enjoyed the way he plays."
Murray, whose baby daughter Sophia was born last year, next faces Dustin Brown, the man who knocked out Nadal two years ago.
German world number 97 Brown came back from a set and a break down to beat Portugal's Joao Sousa 3-6, 7-6 (7/5), 6-4, 6-4.
Nick Kyrgios, who shocked Nadal at Wimbledon in 2014, won't get another opportunity.
The combustible 20th seeded Australian was 6-3, 6-4 down to France's Pierre-Hugues Herbert when he called it quits on Court Three after failing to shake off the hip injury which has plagued him in recent weeks.
"I kind of knew I was in trouble. I have been feeling my hip ever since I fell over at Queen's Club," Kyrgios said.
"Never got it right. I was doing everything I could to help it, but just not enough time. Yeah, I mean, I just wasn't 100 percent.
Kei Nishikori, the Japanese ninth seed, beat Italy's Marco Cecchinato 6-2, 6-2, 6-0 in just 72 minutes.
French 12th seed Jo-Wilfried Tsonga, twice a semi-finalist, eased past British wild card Cameron Norrie 6-3, 6-2, 6-2.
Sam Querrey of the United States, who stunned Novak Djokovic in the third round last year and precipitated the Serb's slide from the top, also made the second round.
The 24th seed saw off Italy's Thomas Fabbiano 7-6 (7/5), 7-5, 6-2.
- Win for under-pressure Venus -
Women's second seed Simona Halep, blasted off court in the French Open final by Jelena Ostapenko, downed New Zealand qualifier Marina Erakovic 6-4, 6-1.
Halep, a Wimbledon semi-finalist in 2014, next faces Brazil's Beatriz Haddad Maria.
Venus Williams marked her 20th Wimbledon anniversary with a 7-6 (9/7), 6-4 win against Belgium's Elise Mertens.
The 37-year-old five-time champion arrived in London facing a wrongful death suit after she was involved in a fatal car crash in Florida.
An elderly man in the other vehicle suffered head injuries in the collision and died on June 22.
Williams will face China's Wang Qiang for a place in the last 32.