Federer, a six-time winner in Melbourne, came back from down 8-4 in the fifth set tie break to win 4-6, 7-6, 6-4, 4-6, 7-6 (10-8).
“Oh, God, it was tough,” Federer said.
Millman was two points away from victory, but the 30-year-old Brisbane, Australia, native saw Federer rattle off six straight points in the first-to-10 tiebreaker for the victory.
“It came down to the wire at the end. A bit of luck, maybe. I had to stay so focused,” Federer said of staring down the man who knocked him out of the 2018 US Open. “He kept on coming up with the goods. … I was getting ready to explain myself in the press conference.”
Federer’s biggest issue was his forehand, for so long one of the secrets to his success. It deserted him completely for stretches, and he finished with a whopping 48 of his 82 unforced errors from that shot.
Novak Djokovic had a much easier time at Rod Laver Arena on Friday.
In the match following Serena Williams‘ upset loss to China’s Wang Qiang, the second-seeded Djokovic easily defeated Yoshihito Nishioka 6-3, 6-2, 6-2 to move on to the fourth round of the Australian Open.
Djokovic, a seven-time Australian Open champion, needed only 85 minutes to beat Nishioka. Djokovic had 17 aces and won 43 of 46 points on his first serve (93.5%), his highest percentage of first-serve points won in a completed major match. At one point, he won 34 consecutive points on his serve.
With the win, it is the 50th time Djokovic has reached the round of 16 at a major, second most among men in the Open era after Federer.
Cilic, who won the 2014 US Open and was a finalist here in 2018, defeated ninth-seeded Bautista Agut 6-7 (3), 6-4, 6-0, 5-7, 6-3 to advance to the fourth round.
Bautista Agut beat Cilic here last year in the fourth round and also won in 2016 in the third round.
The 39th-ranked Cilic is unseeded at a Grand Slam tournament for the first time since the 2014 Australian Open. He will next play Milos Raonic, who authored a 7-5, 6-4, 7-6 (2) victory over the sixth-seeded Stefanos Tsitsipas.
Raonic, a 2016 Wimbledon finalist, had five match points in the third-set tiebreaker and converted his second with a booming forehand winner for the victory on Margaret Court Arena.
Seeded 32nd, Raonic finished with 19 aces and 55 winners in a dominating performance against Tsitsipas, who beat Federer here last year on the way to the semifinals.
Raonic’s best run in Australia was to the last four in 2016, when he became the first Canadian man to reach the semifinals at Melbourne Park. He lost that match and the Wimbledon final later that year to Andy Murray.
Raonic missed the French and US Open tournaments last year with injuries but says he’s feeling better after an offseason in which he could focus on recovery.
“It’s fun to be healthy, to be playing well,” Raonic told the crowd. “I can really take a lot of pleasure in that.”
Unseeded Marton Fucsovics took out
The Associated Press contributed to this report.