In a first-round match, Roddick was 7-5, 6-1 winner against Canadian Frank Dancevic.
Elsewhere, Kristian Pless of Denmark beat defending champion and third-seeded Andy Murray of Britain, 6-0, 6-7 (5-7), 6-4; No. 2 seed James Blake of the United States beat Russia's Igor Kunitsyn 6-3, 6-2; No. 5 seed Mardy Fish of the U.S. topped Russia's Teimuraz Gabashvili 6-3, 6-2; sixth-seeded German Benjamin Becker got past qualifier Dusan Vemic of Serbia, 6-4, 3-6, 6-4; and Spain's Feliciano Lopez topped German Rainer Schuettler 7-6 (7-1), 6-1.
Roddick and Blake are trying to build upon their successes last week when the U.S. recorded a 4-1 Davis Cup victory against the Czech Republic.
NBC reportedly holds celebs hostage to Jimmy Fallon's show
Ray Liotta sues skin care company over use of likeness