Nadal, coming off back-to-back Masters titles in Montreal and Cincinnati, improved to 16-0 on hard courts this year with a 6-4, 6-2, 6-2 triumph over American Ryan Harrison at Arthur Ashe Stadium.
The Spanish star's only U.S. Open title came in 2010. He was runner-up the next year but skipped last year's edition with a knee injury.
Japan's Nishikori, meanwhile, was upended by British qualifier Daniel Evans 6-4, 6-4, 6-2, in a 1-hour, 57-minute affair.
Nishikori won the Memphis indoor event in February.
Two other seeded players joined him in the upset column Monday. No. 27 Fernando Verdasco of Spain was done in by Croatia's Ivan Dodig 6-3, 7-5, 1-6, 4-6, 6-3, and 30th-seeded Ernests Gulbis of Latvia fell to Austria's Andreas Haider-Maurer 3-6, 6-3, 1-6, 7-6 (7-4), 6-4.
The news was better for fourth-seeded David Ferrer, however, as the Spaniard overwhelmed Australian Nick Kyrgios, 7-5, 6-3, 6-2, while No. 8 Frenchman Richard Gasquet dispatched American Michael Russell, 6-3, 6-4, 6-2.
Elsewhere in Day 1 action, 18th-seeded Serb Janko Tipsarevic advanced when Uruguay's Pablo Cuevas retired while trailing 6-3, 6-7 (5-7), 6-3, and No. 23 Feliciano Lopez of Spain outlasted Frenchman Florent Serra 6-7 (4-7), 6-2, 6-3, 6-3.
A scheduled match between seventh-seeded Swiss Roger Federer and Slovakia's Grega Zemija was postponed until Tuesday due to rain.