The second-seeded Roddick of the United States breezed past Swiss qualifier Michael Lammer 6-4, 6-2, 6-2 in the nightcap at the first Grand Slam event of the year.
The Wimbledon runner-up Roddick will meet South African Wesley Moodie in the second round.
The fourth-seeded Argentine Nalbandian, the surprise Tennis Masters Cup champion in November, struggled to get past Thai Danai Udomchoke in five sets at Laver Arena, 6-2, 6-2, 1-6, 6-7 (4-7), 6-1. Udomchoke took a timeout because of a back injury in the third set, and Nalbandian wound up going untested in the deciding stanza.
"It's not the best way to start, but is good always to win," Nalbandian said after escaping Udomchoke.
Up next for Nalbandian will be Swiss Stanislas Wawrinka.
Notable deaths of 2014 [PHOTOS]