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.
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.
"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.
- 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.
Later Monday, Nadal, the champion in 2008 and 2010 and a three-time runner-up, faces Australia's John Millman, the world number 137.
The Spaniard missed last year's championships because of a wrist injury but is back at the All England Club buoyed by his 10th French Open title.
Nadal is bidding to record his 850th tour-level match-win and become just the seventh player in history to reach the landmark.
It's also his 50th match at Wimbledon.
Millman is playing just his second match of the year after missing five months with a hip injury.
Kvitova, whose career was almost ended by the injuries caused fighting off an intruder at her home in the Czech Republic, takes on Sweden's Johann Larsson, the world 53.
In the absence of Serena Williams (pregnant) and Maria Sharapova (injured), Kvitova, boosted by winning the recent Birmingham grass court title, finds herself in the position of favourite for a third title to add to her 2011 and 2014 triumphs.
The two-time Australian Open champion made the semi- finals at the All England Club in 2011 and 2012.
Kim Clijsters, Margaret Court and Evonne Goolagong are the only women to have won a Grand Slam after having a child.
Men's fifth seed Stan Wawrinka, looking to complete the career Slam, faces Russia's Daniil Medvedev.
French Open winner Jelena Ostapenko, the 2014 Wimbledon junior champion, takes on Aliaksandra Sasnovich of Belarus.
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