The win came in Federer's first day match so far at this edition.
"I practiced with him (Fucsovics) for a few days in a row in Switzerland," Federer said. "That helped knowing his strength and weaknesses a little bit. He was not completely the unknown opponent.
"It's (the offseason training with the Hungarian) been a while. I didn't see his matches, I haven't watched him play much on TV.
"The goal for me was really trying to be focused on my own game and take it to him and play tough. But he hung with me for a long time. So it was a good match."
Federer will next take on old foe -- and punching bag -- Tomas Berdych, who stopped Italian Fabio Fognini 6-1, 6-4, 6-4 to reach the Australian last eight for the seventh time in eight years.
Federer stands an overwhelming 19-6 in the series, and has faced the Czech at the last two Melbourne editions. The Swiss has won their last six matches.
American Tennys Sandgren, a loser the last four years in qualifying, continued a spectacular debut with an upset of fifth seed Dominic Thiem 6-2, 4-6, 7-6 (7-4), 6-7 (7-9), 6-3.
The 26-year-old ranked 97 denied the Austrian a chance at his first Australian quarterfinal in a struggle of almost four hours.
On the women's side, top seed Simona Halep says she is paying no more attention to her injured ankle after defeating Japan's Naomi Osaka 6-3, 6-2 for a quarterfinal spot.
"It was way better match today. I'm really happy that I could find the rhythm back because is not easy when you are very tired," Halep said. "The ankle is still sore. But I'm not thinking about that any more. I saw that I can win matches with it, so now I'm not that worried any more."
Former Australian Open champion Angelique Kerber beat Taiwan's Hsieh Su-Wei 4-6, 7-5, 6-2.
The German, who won the title in 2016 and later that season earned the world No. 1 ranking, will play for the semis against U.S. Open finalist Madison Keys after the American stunned French eighth seed Caroline Garcia 6-3, 6-2.
Kerber's win ended Hsieh's hopes of knocking out a second Grand Slam champion at the event, after the 32-year-old defeated reigning Wimbledon winner Garbine Muguruza in the second round.
Kerber advanced in just over two hours with 31 winners and six breaks of serve from 13 chances against her 88th-ranked opponent.
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