An easy 6-4, 7-6(4), 6-2 win helped Swiss mogul Federer beat Canada's 13th seed Milos Raonic.
The 17-time Grand Slam champion conceded only five points on his first serve and hit 34 winners to make the last eight for the 35th straight Grand Slam.
Federer wrapped up the first set when Raonic netted a volley, the second with a forehand down to the line to win the tiebreak 7-4.
Chasing his fifth title at the Melbourne Park, the Swiss will meet seventh-seeded Frenchman Jo-Wilfried Tsonga, a finalist here in 2008.
The 22-year-old Raonic, seeded 13th, missed another chance to be the first Canadian to make a Grand Slam quarter-finals in the Open Era.
Williams took only 57 minutes to beat Russia's No.14 seed Maria Kirilenko 6-2, 6-0. It's the eighth time for the 15-time Grand Slam champion to be in the last eight at Australian Open.
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Williams twisted her ankle in her first round clash against Romania's Edina Gallovits-Hall, but still breezed through the first three rounds at Melbourne Park, dropping just six games.
The victory was Williams' 40th from her past 41 matches and she will meet 19-year-old fellow American Sloane Stephens in Wednesday's quarter-finals.
Stephens qualified for her maiden Grand Slam quarter-finals with a 6-1, 3-6, 7-5 win over Serbian Bojana Jovanovski earlier in the day.
Another women's quarter-finals will be played between defending champion Victoria Azarenka and two-time Grand Slam winner Svetlana Kuznetsova.
Azarenka, the World No.1, triumphed over unseeded Russian Elena Vesnina 6-1, 6-1.
Kuznetsova outlasted former World No.1 Danish Caroline Wozniacki 6-2, 2-6, 7-5. The unseeded Russian, the lowest ranked player left in the tournament, showed she was free of the leg injury that ruined her 2012 season.
In other men's fourth round matches, third-seeded Andy Murray scored a 6-3, 6-1, 6-3 win over Frenchman Gilles Simon and will play in the quarter-final unseeded Jeremy Chardy, who beat Italian Andreas Seppi 5-7, 6-3, 6-2, 6-2.
Chardy was joined by fellow-Frenchman, seventh-seeded Jo-Wilfried Tsonga, who beat another compatriot Richard Gasquet 6-4, 3-6, 6-3, 6-2.