The sixth-seeded Swiss crushed Russia's Teymuraz Gabashvili 6-2 6-2 6-3 to make it through to the last 16 of a grand slam without dropping a set for the 27th time in his career.
Federer, 32, next plays the winner of the match between Jo-Wilfried Tsonga, who the Swiss beat over five tough sets in the Melbourne quarter-finals last year, or another Frenchman, Gilles Simon.
"This is clearly a tough draw," he told reporters. "But the important thing now for me is just that I keep playing well and I don't go crazy about who I play now.
"It's just now up to me to bring it in the next match."
Only two of Federer's record 17 grand slam titles have come in the past four years, in Australia in 2010 and at Wimbledon in 2012.
The Swiss has made a habit of demolishing his opponents in the early stages and said the move from 16 to 32 seeds may have helped his cause.
"I have had tough draws throughout my career, not every time, but in many tournaments. So I remember tough draws in early rounds," he said.
"With the 32 seeds it's a bit more predictable, a lot more predictable actually.
"That's one of the reasons I think I have always been able to go deep in slams, especially once I was able to be seeded. I took advantage of that."
Federer was barely troubled by Gabashvili, the world number 79, and though he knows he needs to lift his game, is happy with his form.
"I'm happy that I'm winning my matches in straight sets," he said.
"It's been different conditions every match. The heat first and the indoor match, and now normal conditions today with a bit of wind.
"So it's just good to get through and get a good feel out there and make sure to win your matches easily if you have a chance. That's what I was able to do today, so I'm pleased."
(Editing by John O'Brien)
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