The 17-time Grand Slam champion, seeded a lowly-by-his-standards 17th after spending six months on the sidelines to let his left knee heal, only needed 90 minutes to beat Tomas Berdych 6-2, 6-4, 6-4 in the third round on Friday.
This was against a highly-credentialed pro, seeded No. 10, who beat Federer in the Wimbledon quarterfinals in 2010 on the way to the final. Berdych reached the quarterfinals or better in Australia the previous six years, and had beaten Federer in six of their previous 22 matches.
Federer said he felt like he struggled against the qualifiers in his first two rounds, and knew the degree of difficulty would rise sharply. Having beaten Berdych, he next faces No. 5 Kei Nishikori. And there's a potential quarterfinal match against top-ranked Andy Murray.
"It's just crazy how quick I got out of the blocks," Federer said of his almost flawless match against Berdych. "What a difference it was in the feeling afterward. I did surprise myself.
"From the baseline, honestly, I felt worlds better than in the first couple of rounds."
Federer hit some classic one-handed backhand winners, including one that earned a hearty applause from the great Rod Laver — sitting in the crowd at the stadium named in his honor — in the second set.
He had 40 winners and won 95 percent of points when he got his first serve into play. He didn't face a break point.
During his on-court interview, Federer acknowledged Laver, the last man to complete the calendar year Grand Slam.
Laver waved back.
"It's always nice when he shows up to watch," the 35-year-old Federer said. "It's always nice when he's in the building."
"Guess I'm ready. There's no turning back," Federer said. "He's ... maybe the best backhand in the business right now. Really got my work cut out for me."
Five-time Australian Open runner-up Murray said he had no trouble with his sore right ankle as he advanced to the fourth round for the ninth straight year with a 6-4, 6-2, 6-4 win over No. 31 Sam Querrey.
Murray, who replaced Djokovic at No. 1 in November, said he was surprised at the six-time Australian Open champion's second-round loss to Denis Istomin. But Murray didn't think it changed anything for him.
"I wasn't scheduled to play Novak today, so my job's to concentrate on Sam and to go into that match with a clear head and a good game plan and try to play well," said Murray, who next plays Mischa Zverev. "I did that.
"If you're to get to the final, then it has an effect."
Seven-time major winner Venus Williams routed Duan Yingying 6-1, 6-0 in 59 minutes to reach the fourth round in Australia for the 10th time.
"It's good (but) it's never enough," she said, looking ahead to her fourth-round match against Mona Barthel. "I've tasted it before and it's always a great feeling because it means, hey, I have an opportunity for the quarterfinals. That's what I'm going to go for."
There's no Americans or Australians remaining in the men's draw. No. 23-seeded Jack Sock followed Querrey out, losing 7-6 (4), 7-5, 6-7 (8), 6-3 to No. 12 Jo-Wilfried Tsonga. Daniel Evans beat Bernard Tomic 7-5, 7-6 (2), 7-6 (3).
Women's champion Angelique Kerber beat Kristyna Pliskova 6-0, 6-4 and will next play CoCo Vandeweghe, who had a 6-4, 3-6, 7-5 win over 2014 Wimbledon finalist Eugenie Bouchard. French Open champion Garbine Muguruza closed out Day 5 with a 6-4, 6-2 win over Anastasia Sevastova.
The day belonged to Federer, though, and he didn't mind that everyone noticed. When reminded in his news conference of his range of exquisite shots, the 35-year-old Swiss star eased into his chair and nodded.
"Thank you. Keep going. Keep going — it's good, it's good," he said, smiling. "What's nice about tonight is it was unexpected for me, unexpected for a lot of people apparently as well, and it was against a fellow top player."