Nadal, the second-seeded 2010 champion who watched the 2012 US Open from his home in Spain as he endured a seven-month injury layoff, cruised to a 6-4, 6-2, 6-2 win over America's Ryan Harrison to record a 16th win on hard courts this year.
The 27-year-old Spaniard has captured nine trophies since his return from injury in February, building up a 54-3 record in the process, and came into New York having won back-to-back Masters titles at Montreal and Cincinnati, comfortably erasing his shock first-round exit at Wimbledon.
"It's a special emotion to be back in New York. It's a special atmosphere," said Nadal, who next tackles either Canada's Vasek Pospisil or Brazilian qualifier Rogerio Dutra Silva.
"I was nervous before the start, but I hope to have these nerves again in the future if it means I win."
Defending women's champion Serena Williams, a four-time winner, needed just an hour to see off Italian veteran Francesca Schiavone, 6-0, 6-1.
The top seed fired 13 winners and broke the former French Open champion six times on her way to a second round match-up against Kazakhstan's Galina Voskoboeva.
"I'm really excited," Williams said. "I knew playing a former Grand Slam champion the first round was a tough draw so I just tried to be super serious."
Venus Williams, the back-to-back champion in 2000 and 2001 and the oldest woman left in the draw at 33, started her 15th US Open with a 6-1, 6-2 win over Belgian 12th seed Kirsten Flipkens, a semi-finalist at Wimbledon.
Williams, now ranked 60th in the world, next faces China's Zheng Jie after avenging a loss to Flipkens at Toronto earlier this month.
"It's just good to be here, see familiar faces since my first time in 1997 with the beads and the braces," said Williams, after firing 21 winners and who dyed her hair purple for the occasion.
Federer, the former five-time champion and seeded a lowly seventh this year, was due to take on Slovenia's Grega Zemjla in the closing match on Arthur Ashe Stadium.
But heavy late evening rain meant the Swiss star, still bruised by his second round loss at Wimbledon -- his worst All England defeat in a decade -- will have to try again on Tuesday.
There were no such problems, however, for Spanish fourth seed David Ferrer, a semi-finalist in 2007 and 2012, who defeated teenage Australian qualifier Nick Kyrgios, 7-5, 6-3, 6-2 and will next play compatriot Roberto Bautista.
British qualifier Daniel Evans, the world number 179, stunned Japanese 11th seed Kei Nishikori, in the day's biggest shock, 6-4, 6-4, 6-2.
The 23-year-old Evans had never won a main draw match at the Grand Slams until Monday and his reward is a second-round clash against Australia's Bernard Tomic, who needed five sets to see off Albert Ramos of Spain.
Monday's win guaranteed Evans at least $53,000 -- $10,000 more than he has made in all of 2013 so far.
"I really want to be top 100, so that's when the money will start to come in, is when I'm top 100 consistently," said Evans.
"It is an added bonus. But it would be a bit strange if I was just thinking about the money after I've just beat the 11th seed."
Fernando Verdasco, the 27th-ranked Spaniard, was beaten by Croatia's Ivan Dodig 6-3, 7-5, 1-6, 4-6, 6-3.
Latvian 30th seed Ernests Gulbis also went out, losing 3-6, 6-3, 1-6, 7-6 (7/4), 6-4 to Austria's Andreas Haider-Maurer.
Polish women's third seed Agnieszka Radwanska, who has never gotten beyond the last-16, eased past Silvia Soler-Espinosa 6-1, 6-2 and next faces another Spaniard, Maria Teresa Torro-Flor.
Chinese fifth seed Li Na also reached the second round with a 6-2, 6-2 win over Olga Govortsova of Belarus.
Li, a quarter-finalist in 2009, next plays Sofia Arvidsson of Sweden.
Laura Robson, the first British woman to be seeded at a major for 26 years, won nine games in succession to beat Spanish veteran Lourdes Dominguez Lino, 7-5, 6-0.
The 30th seed, who ended Kim Clijsters' career in New York 12 months ago on her way to the last 16, next faces France's Caroline Garcia.
There was also an emotional win for Russia's Alisa Kleybanova, with the former world number 20 beating Monica Puig of Puerto Rico, 6-4, 3-6, 7-5, in her first match at a major since beating cancer.