The Swiss second seed was too strong for the 80th-ranked Fucsovics, winning 6-4, 7-6 (7/3), 6-2 in just over two hours on Rod Laver Arena.
Federer will now face long-time rival Tomas Berdych in the last eight, holding a 19-6 lead over the Czech dating back to 2004.
It will also be Federer's 52nd Grand Slam quarter-final, the most in the post-1968 Open Era.
It was the Swiss legend's first meeting with Fucsovics, who spent a week in the off-season training with him in Switzerland.
"Being two sets down is never easy, but I thought he was playing very clean, solid and I had a hard time breaking through until two sets and a break up."
Federer will renew his rivalry with the big-serving Berdych, who powered into the quarters with a straight sets win over Italian Fabio Fognini earlier Monday.
"I saw his matches, he's been hitting the big shots. I am happy for him, he's through his back issues from last year and I had a good match with him here in the third round last year," Federer said.
Federer's latest victory was his 91st in Melbourne to make the Australian Open his joint most successful Grand Slam in terms of matches won along with Wimbledon.
He wasn't expected to encounter too much trouble with Fucsovics and so it proved with three service breaks, and no break points on his own service along with 34 winners.
Federer is coming off an extraordinary 2017, when he won a fifth Australian Open title and a record eighth at Wimbledon, after returning from an injury lay-off.
It was in Melbourne a year ago where he lit the fuse on his late-life tennis renaissance, beating Berdych, Kei Nishikori, Mischa Zverev and Stan Wawrinka before downing great rival Rafael Nadal in a five-set final classic.
Disclaimer: No Business Standard Journalist was involved in creation of this content
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
