Seven-time champion Federer reached his 13th All England Club quarter-final with a 6-2, 6-2, 6-3 win over Spain’s Roberto Bautista Agut, while Murray defeated giant Croatian Ivo Karlovic 7-6 (9/7), 6-4, 5-7, 6-4.
Djokovic, in danger of becoming the first top seed since Pete Sampras in 2001 to lose in the last 16, stood at 6-7 (6/8), 6-7 (6/8), 6-1, 6-4 against 14th seeded South African Anderson when play was suspended on Court One with the fourth round clash to be completed Tuesday.
Should the world number one achieve his fourth career victory from two sets down, he would face US Open champion Marin Cilic for a semi-final spot.
The 33-year-old Federer needed just 96 minutes to clinch victory over Bautista Agut and goes on to face French 12th seed Gilles Simon for a place in the semi-finals.
Federer holds a 5-2 career lead over Simon, who reached his maiden All England Club quarter-final by knocking out 2010 runner-up and sixth seed Tomas Berdych.
The Swiss star claimed victory on a sixth match point against Bautista Agut, whose challenge was seriously compromised by needing treatment on his right ankle after a bad fall in the sixth game of the second set.
“He definitely didn’t have the best fall in the second set, I was happy that he was able to continue to play,” said Federer.
“I’m sure Gilles is happy to be in the quarters but I hope to stop that run now.”
British third seed Murray claimed a 7-6 (9/7), 6-4, 5-7, 6-4 win over 2.11-metres (six feet, 11 inches) tall Karlovic to book his place in the quarter-finals for the eighth successive year.
Murray, the 2013 champion, will next face unseeded Canadian Vasek Pospisil.
Karlovic, at 36 the oldest man to reach the last-16 in 39 years, fired 29 aces in the three-hour Centre Court encounter, but that was well below par for a man who had blasted 136 in his first three rounds.
Murray hit 62 winners to the Croatian’s 75 but crucially only nine unforced errors to his rival’s 32.
“I came up with some good lobs and passing shots. I just needed to keep him low,” said Murray.
“It was an incredibly difficult match, it was mentally tiring because you just have to be ready when the chances come.”
French 21st seed Richard Gasquet defeated Nick Kyrgios 7-5, 6-1, 6-7 (7/9), 7-6 (8/6) in a controversial clash to avenge a second round loss to the temperamental Australian in 2014.
The 29-year-old, a semi-finalist in 2007, will next face fourth seed Stan Wawrinka after winning a last-16 clash at the majors for just the third time in 19 attempts.
But Gasquet’s win was overshadowed by the latest controversy surrounding 20-year-old Kyrgios, the man who knocked out Rafael Nadal 12 months ago.
He tanked the third game of the second set — allowing Gasquet four uncontested points — after arguing with umpire James Keothavong over a code violation for swearing, a gesture which brought boos from the crowd.
Kyrgios also argued with the official over the length of time he was taking to change his socks.
“Of course I tried. I moved (for the ball),” insisted Kyrgios in a combative press conference where he jousted with reporters.
“If they decide to fine me, they can fine me. Just because I show emotion out on the court, I’m bad. So, whatever.”
French Open champion Wawrinka defeated Belgian 16th seed David Goffin 7-6 (7/3), 7-6 (9/7), 6-4 to reach the quarter-finals for the second successive year.
Wawrinka is bidding to become just the fifth man to win Roland Garros and Wimbledon in the same year.
Pospisil became only the third Canadian man to reach the quarter-finals with a 4-6, 6-7 (4/7), 6-4, 6-3, 6-3 win over Serbian 22nd seed Viktor Troicki.
It was the world number 56’s third five-set match in four rounds and his first career comeback from two sets to love down.
Simon reached the quarter-finals for the first time with a 6-3, 6-3, 6-2 defeat of Berdych.
It will the 30-year-old Frenchman’s first last-eight spot at a major since the 2009Australian Open.
Cilic made the quarter-finals for the second successive year with a 6-4, 4-6, 6-3, 7-5 win over unseeded American Denis Kudla.
The 28-year-old Cilic will be hoping Anderson stuns Djokovic as he has a 12-0 losing record against the Serbian world number one.