The Swiss four-times champion was in sublime form as he won 6-2 6-1 6-4 to progress to the last eight Down Under.
Defending champion Novak Djokovic, meanwhile, survived a scare as he made 100 unforced errors during a 6-3 6-7 (1-7) 6-4 4-6 6-3 win over Gilles Simon after four hours and 32 minutes on Rod Laver Arena.
Djokovic will take on Japan’s Kei Nishikori in the last eight, while third seed Federer plays Tomas Berdych.
“Playing against a player like Gilles you can expect a lot of rallies,” said Djokovic, who is through to his ninth successive Australian Open quarter-final.
“He is always making you play an extra shot.
“I made a lot of unforced errors today but he was fighting, he was playing well, physically it was very demanding and I’m just happy to get through this one.”