The result extended Federer's run of consecutive sets won at Wimbledon to 32, two short of his career best from 2005-06, while he has not dropped serve since the semi-finals previous year. Speaking about how his game perfectly suits the court condition at the All England Club, Federer said: 'Maybe it's that it helps my slice.
Rafael Nadal has breezed into his first Wimbledon quarter-final since 2011.
Russia's Ekaterina Makarova defied second round victim Wozniacki's churlish prediction that she wouldn't progress further in the tournament by reaching the last 16.
"I didn't think that was ever going to happen, to be honest", Federer said after setting up a last eight meeting with another Frenchman, Gael Monfils, or South African eighth seed Kevin Anderson.
The eight-time champion needed only 16 minutes to win the first set against France's Adrian Mannarino.
Had the Swiss not squandered four break points in the opening game of the second set, which lasted nearly as long as the entire opener, Federer would probably have not needed an hour and 45 minutes to get back into the locker room.
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He then shocked supporters when he ended up jumping onto the bus stop, shattering the glass roof and knocking over a bystander. He branded such behaviour a "total disgrace". "Owed it to the fans back home who believed in us", he told the BBC.
World number one Rafael Nadal took to the practice courts ahead of his last-16 tie with Jiri Vesely on Monday - and soon found himself in very familiar company. His problem has always been the first week of Wimbledon, not the second week.
The blow appeared to suck the life out of Mannarino and he was broken in the next game before Federer served out for the match.
Williams will equal Margaret Court's record of 24 Grand Slam titles if she wins Wimbledon for the third time in the last four years. Another statistic that makes this one seem like quite a mismatch: Federer is 5-0 against Mannarino, winning 12 of the 13 sets they've played.
The Latvian player also reached the quarterfinals a year ago in her best Wimbledon showing, losing to eventual runner-up Venus Williams.
At 1-1 in the third, Federer saw an opportunity to break at 30-0 but Mannarino held his nerve to hold.
One by one, Federer, Nadal and Djokovic - 49 grand-slam titles between them - all strolled out from the pavilion to camera shutters frantically clicking, before beginning their hour-long hits next to each other.