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.
"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.