The seven-time champion achieved his double landmark by seeing off Steve Johnson of the United States 6-2, 6-3, 7-5 in the fourth round on Centre Court.
Federer, the third seed, next takes on Croatia's Marin Cilic for a place in the semi-finals.
Cilic, the ninth seeded Croatian, progressed to his third Wimbledon quarter-final when Japanese fifth seed Kei Nishikori pulled out of their last-16 clash with a rib injury in the second set.
Federer has a 6-1 record over Cilic but the big Croatian stunned the 17-time major champion in the US Open semi-finals in 2014 on his way to his maiden Grand Slam title.
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Johnson, the champion on grass at Nottingham this summer and playing in his first fourth round at a Slam, was comprehensively out-played in the first two sets.
He rallied to break the 34-year-old Federer in the fourth and sixth games of the third set but the former American college champion was reeled in on both occasions.
"Best of five matches are always tough," added Federer, whose 14th appearance in a Wimbledon quarter-final matches the mark of Jimmy Connors.
Federer has reached the last eight without dropping a set, easing to four successive wins on Centre Court.
"I would never have thought I would win the first four rounds in straight sets. I now need to play my best tennis."
- Injury woe -
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Nishikori pulled out against Cilic suffering from a rib injury at 6-1, 5-1 down.
"It got worse after the second round. I couldn't compete today," said Nishikori.
Cilic had taken the first set in just 16 minutes, allowing Nishikori only seven points.
Sam Querrey followed up his shock defeat of Novak Djokovic by beating French veteran Nicolas Mahut 6-4, 7-6 (7/5), 6-4 to reach his first Grand Slam quarter-final.
Querrey, the 28th seed, is the first American in the last-eight at Wimbledon since Mardy Fish in 2011.
He will face either Canada's Milos Raonic or David Goffin of Belgium for a place in the semi-finals.
Murray has a 4-0 career lead over the Australian with three of those meetings having come in the majors.
Richard Gasquet and Jo-Wilfried Tsonga meet in an all-French duel. Both men are two-time semi-finalists at the All England Club.
In an all-Czech match-up, world number 64 Jiri Vesely, who beat Djokovic in Monte Carlo this year, takes on 10th seed and 2010 runner-up Tomas Berdych.
It will be Vesely's first appearance in a Slam fourth round.