The Swiss, looking to climb back into the world's top four after a poor 2013, dropped six games against Finland's Jarkko Niemenen, winning 6-4 6-2 in the second round as he looked untroubled in the Pat Rafter Arena.
Federer will come up against a home favourite in the next round in the shape of Marinko Matosevic.
In what was his first tour victory on an Australian court, the Bosnia-born 28-year-old saw off the big-serving Sam Querrey 5-7 7-6 (7/3) 6-4.
One Australian did go out, though, with Matthew Ebden disappointing as he lost 6-2 6-4 to second seed Kei Nishikori.
Maric Cilic continued his comeback from a doping ban with an impressive win over Grigor Dimitrov, the fifth seed, while in the women's draw, Angelique Kerber was close to victory against Anastasia Pavlyuchenkova when her opponent retired hurt.
Maria Sharapova also benefitted from a withdrawal as Ashleigh Barty could not take to the court because of a stomach problem, with the same fate striking Sabine Lisicki, with the Wimbledon finalist pulling out sick.