Seeded second in New York, Djokovic needed only 73 minutes to dispatch Italian Paolo Lorenzi, 6-1, 6-0, 6-1, while 20th-seeded Roddick, a former U.S. Open winner, smashed 20 aces en route to 6-3, 6-4, 6-4 defeat of fellow American and qualifier Rhyne Williams.
Also Tuesday, fifth-seeded Frenchman Jo-Wilfred Tsonga, who reached the quarterfinals at last year's event, bested Slovakia's Karol Beck 6-3, 6-1, 7-6 (7-2).
In other action involving seeded players, No. 6 Tomas Berdych of the Czech Republic got past Belgian David Goffin 7-5, 6-3, 6-3 and No. 11 Nicolas Almagro of Spain defeated Czech Radek Stepanek 6-4, 6-7 (5-7), 6-3, 6-4.
Fifteenth-seeded Milos Raonic of Canada posted his first career U.S. Open main draw triumph, outlasting Colombian Santiago Giraldo 6-3, 4-6, 3-6, 6-4, 6-4, while No. 18 Stan Wawrinka of Switzerland doused Ukrainian Sergiy Stakhovsky 6-7 (6-8), 7-6 (7-2), 6-4, 6-2.
Meanwhile, 10th-seeded Argentine Juan Monaco was bounced in an upset by Spain's Guillermo Garcia-Lopez 3-6, 1-6, 6-4, 7-6 (8-6), 7-6 (7-3).
Other Day 2 winners included No. 31 seed Julien Benneteau of France, American Sam Querrey, Taiwan's Jimmy Wang, Belgian Steve Darcis, Spaniard Pablo Andujar, German Philipp Petzschner and Russian-born American Dennis Novikov.
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