The 34-year-old overcame some feisty second set resistance from Alexandr Dolgopolov before he ran away with the match 6-3 7-5 6-1 courtesy of a superb service game and aggressive groundstrokes in the final set.
He will next play Bulgaria's Grigor Dimitrov in the third round on Friday and the third seed was so far enjoying his quest for his fifth Australian Open title.
"It's been going very well for me, and I hope to keep it up as long as I choose to play tennis," the 17-times grand slam winner told reporters after recording his 299th victory at a grand slam with the win against the 27-year-old Ukrainian.
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"The least I expect (is) to be in the third round of a slam, so I'm pumped up, playing well, feeling good."
Federer said while he was still in love with the sport that had earned him hundreds of millions of dollars in prize money and endorsements, he may resist the idea of following any of his four children if they turned professional.
"I think it's 40 years on the tennis tour that doesn't excite me, you know, straight," he said while laughing when asked to clarify an on-court statement he made about not wanting to watch his daughters play on Rod Laver Arena.
"As much as I love it now, I'm just not sure what my excitement level will be in 20 years' time from now."
Federer, who has six year-old twin daughters Myla Rose and Charlene Riva and twin boys Leo and Lennart, who were born in May 2014, said he had encouraged his daughters to take tennis lessons for reasons other than carving out a potential career.
"I think it's a good thing for them," he said.
"It's a great sport to learn how to lose, to win, to figure it out, for friendship, discipline, for hand-eye coordination.
"I will support them all the way whatever they want to do, but I don't see myself doing that right now.
"I'd rather support them in another sport. Go see them be a super skier. That would be exciting.
"To go watch tennis matches, I don't know," he laughed again.
(Editing by John O'Brien/Amlan Chakraborty)
