Switzerland's Federer, the tennis tournament's defending champion handled German Bjorn Phau 7-5, 6-0, 6-4 in straight-sets at Rod Laver Arena.
American Roddick, the former world No. 1 player, needed four sets to oust French wild card Jo-Wilfried Tsonga, 6-7 (18-20, 7-6 (7-2), 6-3, 6-3.
In other matches, Mardy Fish of the United States downed fourth-seeded Ivan Ljubicic of Croatia, 4-6, 7-6 (7-2), 6-4, 6-4. Ljubicic reached the quarterfinals at least year's Australian Open.
Last year's runner up, 11th-seeded Cypriot Marcos Baghdatis beat Rainer Schuettler of Germany, 6-4, 2-6, 6-3, 6-2 in a first-round match.
2014: The Year in Music [PHOTOS]