The Serbian star, who fell to Andy Murray in the title match of last year's New York event, cruised to a 6-1, 6-2, 6-2 blowout of Lithuania's Ricardas Berankis in an 81-minute affair.
Federer, meanwhile, prevailed 6-3, 6-2, 7-5 over Slovenia's Grega Zemlja in his opening test at Arthur Ashe Stadium in a match originally set to be Monday's opening-night finale but postponed due to rain.
The Swiss great, winner of five straight U.S. Open crowns from 2004-08, now goes on to face Argentina's Carlos Berlocq, who completed a suspended 6-3, 3-6, 6-7(8-6), 6-4, 6-2 comeback win over Colombia's Santiago Giraldo.
Joining them in the second round will be No. 5 Czech Tomas Berdych, who pounded Italian Paolo Lorenzi, 6-1, 6-4, 6-1, and 13th-seeded American John Isner, who dispatched Italian Filippo Volandri, 6-0, 6-2, 6-3.
Tenth-seeded Canadian Milos Raonic, meanwhile, uncorked 28 aces in his 6-3, 7-6 (8-6), 6-3 first-round triumph over Italian Thomas Fabbiano, and No. 12 German Tommy Haas breezed past Frenchman Paul-Henri Mathieu, 6-4, 6-4, 6-1.
The result wasn't as good for two other seeded players, however, as No. 14 Pole Jerzy Janowicz fell to Argentine qualifier Maximo Gonzalez 6-4, 6-4, 6-2, and No. 15 Nicolas Almagro of Spain was upended by Uzbekistan's Denis Istomin 6-3, 6-1, 4-6, 6-3.
Other Day 2 winners included 22nd-seeded German Philipp Kohlschreiber, Portuguese Joao Sousa, 26th-seeded American Sam Querrey, No. 31 Julien Benneteau and Gael Monfils of France, and Americans Jack Sock, Donald Young and Denis Kudla.