The Swiss star looked in fine form, losing just five points on his serve in the second set against the world number 39.
Federer - who will play Marinko Matosevic in the quarter-finals after Matosevic beat Sam Querrey 5-7 7-6(3) 6-4 - was happy to have a win under his belt as he tries to gauge his form in what is his first tournament appearance in the opening week of the season since the year 2000.
"Most important is that you win the match so you get a second chance to judge your game a bit better," said Federer.
"That's why it's most important to get an extra day or two. Now I have doubles tomorrow and the singles the next day, so it's really good for rhythm and good for your game.
"I expect myself to play a bit better in the next match, even though today was already very good for a first match in so many weeks, to be honest, and against Nieminen who can play very good tennis. Particularly here in Australia."
World number 37 Marin Cilic knocked out fifth seed Grigor Dmitrov 7-5 7-5, earning a quarter-final match against second seed Kei Nishikori.