The six-time champion repeated a victory over the Hungarian from the 2018 edition with his win to cap the Australia Day holiday.
After dropping the opening set, the Swiss icon lost just five more games, striking more than 40 winners
The third seed ended it after two hours, 10 minutes with a serve winner on his third match point.
The winner of a record 20 Grand Slam singles titles reached the last eight at a major for the 57th time.
“It was a tough start, he played clean,” Federer said. “I struggled to put the (dramatic, four-hour) Millman match behind.
“It took some time, I was looking to mix it up a bit more. The court is really slow at night, especially in these cooler temperatures.
“I just had to figure it all out.”
The 38-year-old added: “I got off to a good start in the second set, form then on things got a bit easier.”
Federer will aim for the semi-finals against Tennys Sandgren after the American outlasted Fabio Fognini 7-6(5), 7-5, 6-7(2), 6-4.
Novak Djokovic moved a step close to an eighth Open title as he dismissed Diego Schwartzman 6-3, 6-4, 6-4.
Djokovic will be competing in his 46th Grand Slam quarter-final when he plays Milos Raonic after the Canadian defeated former finalist Marin Cilic 6-4, 6-3, 7-5,
He completed his workout in just over two hours with four breaks of serve.
“I had a fantastic couple of matches in a row, center court, last two rounds,” Djokovic said. “I felt more confident going through the ball hitting serves really well.
“Today was a good test because Diego was in form, he hasn’t dropped a set in three rounds. He he can be a very dangerous opponent from the baseline if you give him time.
“I kept things pretty much in control in all three sets. All in all, it was a very solid performance.”
Raonic, who played a Melbourne semi-final four years ago, turned in a 35-ace performance against the 2018 finalist.
“It’s always been very positive for me here, and I always found a way to play well.
“Being fresh physically and mentally at the start of the year and having some time to train in the off-season, does me a lot of good.
The Canadian who was born in Montenegro has never beaten Djokovic in nine previous meetings, the last in 2018.
“I’m going to have to serve well clearly, and I’m going to have to get my return at a high percentage, make him play a lot of those points.
“He’s done a good job in the past neutralising my serve. So I have really got to focus on my things well and be the one dictating.”
Raonic, who managed to front up for only 14 events during an injury-plagued 2019, had to be content with a highlight pair of semi-finals last season.
Djokovic, who has lost only one set so far at this edition, was untroubled by Argentine Schwartzman, who now stands 0-4 against the second seed.
“He’s one of the quickest guys on Tour,” Djokovic said, “i tried to mix up my game and it worked very well.”
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