Federer beat American Steve Johnson 6-2 6-3 7-5 to equal Martina Navratilova’s record 306 grand slam singles victories while Murray knocked out brash Australian Nick Kyrgios 7-5 6-1 6-4.
It means the pair are now just two wins away from a repeat of the 2012 final at the All England Club, when Federer beat Murray in four sets to clinch his last major.
Murray is up against Jo-Wilfried Tsonga next while Federer faces Marin Cilic, having reached the last eight 14 times, an achievement that levels the Open era record held by Jimmy Connors.
“It’s probably going to be something I’m happy I achieved looking back when it’s all said and done,” Federer said of his new records.
“I never thought I was going to have such a great career here at Wimbledon ever since I turned up here in 1998.”
Federer is yet to drop a set at this year’s Championships and while Johnson, ranked 29th in the world, was expected to offer a first real test, the world number three was rarely troubled.
The 17-time grand slam champion will now have to beat Cilic, who won in straight sets when they last met at the US Open two years ago and arrives in good form, having pushed Murray to a decider at Queen’s last month.
“He blew me off the court at the US Open. I know what I’m getting into,” Federer said.
The world number 13 may also have the benefit of fresh legs after he was made to play only 45 minutes against Kei Nishikori before the Japanese retired with a rib injury.
Nishikori was encouraged by his coach Michael Chang to stop earlier but continued for almost two sets before withdrawing at 6-1 5-1 down.
Also in Federer’s half is Canadian Milos Raonic, who came back from two sets down to win for the first time in his career against David Goffin.
Raonic, who is taking advice from John McEnroe this summer, is one of the most dangerous players in the draw but he proved his mettle too on Court Two with a 4-6 3-6 6-4 6-4 6-4 victory.
Raonic will now play Djokovic’s conqueror Sam Querrey, who continued his surprise run with a convincing 6-4 7-6 (7/5) 6-4 win over experienced Frenchman Nicolas Mahut. It is the first time Querrey has ever made a grand slam quarter-final and the 28-year-old also became the first American man to do so since John Isner at the US Open in 2011. Tsonga was only on court for 24 minutes before fellow Frenchman Richard Gasquet retired with a back problem. Gasquet was down 4-2 in the first set.
Meanwhile Serena Williams promised she would never sue Wimbledon after making a “heat of the moment” threat during a fourth-round win over Svetlana Kuznetsova.
The six-time women’s singles champion was unhappy with the suggestion she and her Russian opponent should play on at 5-5 in the first set, after light drizzle fell on Centre Court. She believed it left her open to suffering a slip on the grass that could lead to injury.
After discussing her concerns with umpire Marija Cicak and tournament referee Andrew Jarrett, Williams and Kuznetsova were allowed to leave the court and the retractable roof was deployed to provide cover.
The players were soon able to return and Williams won every game from that stage onwards, for a 7-5 6-0 victory.
When talking initially to Cicak, Williams could be heard to say: “I’m going to fall. Can’t they just close the roof?”
Cicak’s response was inaudible but Williams added: “If I get hurt, I’m suing...”
A ball boy then ran across the court, and slipped badly on the grass, showing that Williams had valid concerns.
In her post-match press conference, Williams was asked about her comments on court. She said: “You guys, don’t even try me like that. I was in the moment, I was on the court, and what I say on the court, whether it’s smashing my rackets, or... it’s in the heat of the moment.
“I have no plans of suing Wimbledon. Like, let’s get serious. That’s not what I do, not what I am, and I’m not answering any more questions about that. Nor will I want anyone reporting that either - that’s completely unfair. Next question.”