The Spaniard, who had not played a tournament match since suffering a knee injury in November, won 6-1, 6-1, 6-1, BBC reported.
"I'm very happy to be back, it's a very important beginning for me," he said.
"I want to enjoy every moment I'm here on this court."
Third seed Grigor Dimitrov and in-form Australian Nick Kyrgios also advanced, but eighth seed Jack Sock was one of 10 American men and women to lose.
Sock went down 6-1, 7-6 (7-4), 5-7, 6-3 to world number 41 Yuichi Sugita, and 16th seed John Isner lost 6-4, 3-6, 6-3, 6-3 to Australia's Matthew Ebden.
Nadal, aiming for a 17th Grand Slam title and a second in Australia, was hampered by a knee injury at the end of the 2017 season.
But the Spaniard, who was beaten by Roger Federer in last year's final, got off to a perfect start and raced to victory over the 37-year-old in 94 minutes on Rod Laver Arena.
The world number one will play Leonardo Mayer of Argentina next.
Bulgarian Dimitrov, 26, went through with a 6-3, 6-2, 6-2 win over Austrian Dennis Novak in one hour 38 minutes.
Kyrgios, the top-seeded Australian in the men's draw at 17, enjoyed a straightforward 6-1 6-2 6-4 victory over Brazil's Rogerio Dutra Silva.
Croatia's sixth seed Marin Cilic beat Canadian qualifier Vasek Pospisil 6-2, 6-2, 4-6, 7-6 (7-5).
Swiss Belinda Bencic sent an early shockwave through the Australian Open on Monday by toppling last year’s finalist Venus Williams on an opening day of carnage for American tennis.
With defending champion and new mum Serena absent, 20-year-old Bencic’s brilliant 6-3, 7-5 win under the Rod Laver Arena roof ensured there would not be a Williams sister in the second round of the tournament for the first time in over 20 years.
It also continued a bleak day for the United States, with three of their four women’s semifinalists from Flushing Meadows last year falling at the first hurdle.
US Open champion Sloane Stephens tumbled in three sets against China’s plucky Zhang Shuai, before 10th seed Coco Vandeweghe was sent packing in two by Hungary’s Timea Babos.
For former world number seven Bencic, victory was another step on an impressive comeback trail from a wrist surgery that saw her tumble out of the top 300 last year before her return in September.
“I think (before) I had a little bit too much respect, played a little bit careful and safe,” Bencic, who was a toddler when Venus won her first grand slam at Wimbledon in 2000, told reporters.
“This time, I really tried to come out and, you know, hit it big. Also tactically be smart on the court.”
Now ranked 78th, Bencic teamed up with Roger Federer to win the Hopman Cup for Switzerland in the lead-up and was thrilled to have the defending champion’s parents watching from her players’ box as she worked over Williams in less than two hours.
Federer’s parents are used to seeing wins and Bencic did not disappoint, playing the 37-year-old American to perfection.
Soaking up the fifth seed’s firepower, she counter-punched brilliantly to seal the match with a pair of rasping forehand winners.