The 19-time Grand Slam winner is yet to lose a set at Melbourne Park this season, seeing off world number 80 Fucsovics 6-4 7-6 (7-3) 6-2.
Second seed Federer, 36, will face Czech Tomas Berdych in the last eight years, that he beat in last year’s third round.
“I am sure he wants to make me cover this one,” said Federer.
“I watched his games, he’s standing up hitting big shots and I am glad he’s back.”
The Swiss were in excellent form on Rod Laver Arena, playing at the day session for the first time in 2018, as he made quick work of Fucsovics to win in 2 hours, one minute.
“Playing at night, going to bed at 3 am, is a different rhythm to playing in the summertime,” he added.
It required Federer four break points to earn an advantage in the first set, before taking the second onto a tie-break.
But the five-time Australian Open winner broke early in the next and followed up with another break of serve to prepare a replica of last year’s third round.
Berdych, the 19th seed, made his place in the last eight with a 6-1 6-4 6-4 triumph over Italy’s Fabio Fognini.