The defending champion made it 32 straight sets won at the All England Club with a 6-0 7-5 6-4 victory over Adrian Mannarino to reach the last eight for the 16th time.
The last time he won as many consecutive sets was in 2005 and 2006, at the height of his dominance.
Federer said: “I feel like these streaks just happen. You can’t plan for them anyway because one point can change the outcome of a set. Of course, if you give yourself maximum chances, you’re playing well, you have super focus, then these streaks are kind of possible.
“I’m equally happy if I would have won all the matches in four sets. That it happened to be in straights, it helps me for the season, to save energy, it helps me to save energy for the rest of the tournament.
“I don’t think it’s something anybody aims for, to win every match in straight sets. It’s like today, I hope I get off to a good start, go from there. If it happens, it happens. It shouldn’t be a shock, and, ‘Oh, my God, I can’t believe it, I lost a set’. It’s part of what a tennis match is about.”
Even by Federer’s stratospheric standards, the first set was a little absurd. Of the five points he lost in the 16-minute opener, three were in the final game, when he faced his first break point of the tournament – and answered it with an ace.
After that things became a little trickier, and Federer was in danger of losing a set when Mannarino had three break points in the eighth game of the third set. But Federer saved all of them before breaking and serving out the victory to love.
The first set was so one-sided that, when Mannarino trailed 0-40 in the opening game of the second, the normally pro-federer Centre Court crowd began to cheer loudly for his opponent.
It had the potential to be embarrassing, particularly given Mannarino is a top-30 player, but the Frenchman composed himself well to make a match of it.
Federer said: “I told my team the other day that for me also, after all these years, it is surprising to be the number one seed, in the top two in the rankings at 36. I didn’t think that was ever going to happen.
“That sometimes there is a set like this against a player who is not the biggest server, it can happen. Then he showed that he is top 30 after all, he played two good sets after that.
“I was also surprised it was that fast, that first set, especially 16 minutes. That was too fast. Shouldn’t really happen, but thankfully they do for me. I probably won’t have another 6-0 set this week, so I’ll enjoy this one.”
The pair’s meeting in Birmingham two weeks ago lasted just 46 minutes, with Osaka sweeping Boulter aside for the loss of only three games.
But the 21-year-old Briton, who secured her first grand slam victory on Tuesday, showed significant improvement from that match to give one of tennis’ brightest rising stars a decent test.
The respectable second-round performance finishes off an excellent grass-court campaign that will see Boulter climb to around 111 in the world rankings a week on Monday.
Boulter immediately looked a lot more comfortable than she had two weeks ago, forcing three break points in the opening game and surprising Osaka with the quality of her backhand down the line.
— Wimbledon (@Wimbledon) July 5, 2018
She could not convert her chances and soon found herself 3-0 down, but self-belief is one of Boulter’s strengths and there were enough errors from the Osaka racket to give the new British number two hope.
Boulter fought back to 3-2 but she was allowing Osaka too many looks at her second serve and the Japanese player immediately got her nose back in front.
The start of the second set again saw Boulter pushing for a break but Osaka, the champion in Indian Wells in March, has loftier ambitions than simply getting through early rounds and looked determined not to allow the match to become complicated.
A loose game from Boulter at 2-2 ultimately cost her as Osaka moved through to round three for the eighth time in her 10 grand slam appearances.
Provided by Press Association Sport
Wimbledon traditionally invites household name sporting personalities to sit in the Royal Box on Centre Court on the middle Saturday of the tournament.
Organisers at the All England Club have stuck steadfastly to plans not to screen World Cup matches this year.
And Press Association Sport understands no provision will be made within the hospitality areas for any of Saturday’s special guests to take in the football.
The England match kicks off at 15:00, while play on Centre Court begins at 13:00.
Former England football captain David Beckham and four 1966 World Cup winners were Royal Box guests on the middle Saturday in 2016.
Sir Bobby Charlton, Sir Geoff Hurst, Gordon Banks and Roger Hunt were all in attendance that day.
British number one Kyle Edmund was in high spirits on Wednesday, lifted by England’s second-round win against Colombia.
He and his Swedish coach Fredrik Rosengren were pictured sparring in rival football shirts.
Edmund tweeted that shot, and Wimbledon revealed another of him strolling in his England top.
The Swedish players in action at Wimbledon were fully into the World Cup spirit, eagerly awaiting their nation’s showdown with England.
Doubles specialist Robert Lindstedt joked Sweden will retain their humility while the whole of England continues to declare football is “coming home”.
“They say that every single championship!” said Lindstedt. “We won’t say that, we’re very humble in our progress, we don’t take anything for granted. We win as a team, we don’t have individuals.
“I don’t think we’re going to win the World Cup, but this is something really to look forward to.
“I watched England-Colombia. It was nice to see how small the English turned as soon as it was penalties.
“But I’m actually happy for them to get through a penalty shoot-out because they’ve suffered a lot.”
Rebecca Peterson lost out to Donna Vekic, with the Croatian prevailing 7-5, 6-4, but the beaten Swede was still able to look forward to the football.
“I hope we can win this one; all the pressure is on England, for sure,” said Peterson.
“There were some supporters out there today wearing Sweden shirts and backing me, and that made me really happy. It really means a lot.
“When the football team does well and wins, you feel really proud of them, and it can boost the whole atmosphere.”
American Madison Keys has thrown her support behind England, thanks to British player Laura Robson.
“I watched England play last night, I was actually watching with Laura,” said Keys. “She was singing the ‘It’s coming home’ song consistently for, like, two-and-a-half hours.
“Where I am staying (in Wimbledon) I can hear the Rose and Crown (pub).
“My TV was ahead of theirs, so something would happen and Laura would scream, and then, like, five seconds later the whole pub would scream. I was actually into it at the very end. So now I’m cheering for England.”