Spain's Rafael Nadal, the No. 2 seed, made his debut at the 2013 U.S. Open with an easy 6-4, 6-2, 6-2 first-round win over American Ryan Harrison.
Nadal's next opponent will be the winner of the match between Brazil's Rogerio Dutra Silva and Canada's Vasek Pospisil.
The match between Dutra Silva and Pospisil was suspended due to rain Monday and will completed on Tuesday.
The 27-year-old Nadal has been on a tear since returning to action in February, playing in 11 finals and winning nine titles.
"Honestly, the last thing I feel is mentally tired, that's not going to be a reason for defeat, if I lose, it's because it was my turn to lose," Nadal said.
Nadal, who won his 8th French Open title on June 9, was off the ATP Tour for seven months due to a knee injury that plagued him after his loss at the 2012 Wimbledon tournament.
"I'm not arrogant, I respect every rival I face and I always go out there nervous. The day when I'm not nervous it'll be because I don't have the same feelings for the sport that I've had all my career," Nadal said.
In other men's action on Monday, Spain's David Ferrer beat Australia's Nick Kyrgios 7-5, 6-3, 6-2, while Spain's Tommy Robredo defeated Australian Marinko Matosevic 6-3, 6-7 (6-8), 6-3, 6-2.
Croatia's Ivan Dodig upset Spain's Fernando Verdasco 6-3, 7-5, 1-6, 4-6, 6-3 and Britain's Daniel Evans upset Japan's Kei Nishikori, the 11th seed, 6-4, 6-4, 6-2.
On the women's side, top seed Serena Williams of the United States crushed Italy's Francesca Schiavone 6-0, 6-1, while American Sloane Stephens, the No. 15 seed, avoided an upset by coming back to beat Luxembourg's Mandy Minella 4-6, 6-3, 7-6 (7-5).
American Venus Williams upset Belgium's Kirsten Flipkens, the No. 12 seed, 6-1, 6-2, while Spain's Carla Suarez Navarro, the No. 18 seed, dismantled American Lauren Davis 6-0, 6-0. EFE