Federer became the oldest man to reach a Grand Slam quarter-final in 28 years when he booked his place in the last-eight for the 17th time.
The eight-time champion breezed past Italy's Matteo Berrettini 6-1, 6-2, 6-2 in just 74 minutes to make sure of a spot in his 55th quarter-final at the Slams.
It was also his 99th win at the All England Club.
At 37, he is the oldest man to reach the last eight at the majors since 39-year-old Jimmy Connors at the 1991 US Open.
Federer, who hit 24 winners and just five unforced errors, will face Japan's Kei Nishikori for a place in the semi-finals.
Defending champion and world number one Djokovic reached his 11th Wimbledon quarter-final and 45th at the majors with a 6-3, 6-2, 6-3 win over France's Ugo Humbert.
Third seed Nadal, the 2008 and 2010 champion, swept to an easy 6-2, 6-2, 6-2 win over outclassed Joao Sousa of Portugal to book his place in a seventh quarter-final at the All England Club.
Between them, the 'Big Three' faced just one break point on Monday and dropped a combined 19 games.
"I'm really getting into a good groove now, today I was able to read his serve, get the returns back in play and hit well from the baseline," said Federer who could face Nadal in a blockbuster semi-final.
"I'm still getting used to the conditions also but on the performance it was a really good match for me."
Japanese eighth seed Nishikori defeated Mikhail Kukushkin of Kazakhstan 6-3, 3-6, 6-3, 6-4 to reach the last eight for the second successive year.
The 29-year-old trails Federer 3-7 in career meetings although he won their most recent clash at the ATP Finals in London at the end of last season.
Four-time champion and top seed Djokovic will face Belgium's David Goffin for a place in the semi-finals.
Djokovic, 32, has a 5-1 career record over 21st seed Goffin who will be playing in his first Wimbledon quarter-final.
Humbert, the world number 66, had never played a match on grass before this season and was defeated in just one hour and 42 minutes.
"My plan always is to reach the final stages at Grand Slams," said Djokovic who converted five of nine break points on Monday.
"Wimbledon has been a special tournament that has motivated me throughout my life."
Nadal next plays Sam Querrey, against whom he holds a 4-1 record.
The 33-year-old Spaniard is chasing his 19th title at the majors, which would put him just one behind the all-time record of 20 held by Federer.
"A lot of positive things out there. To be back in the quarter-finals is great news for me," said Nadal who took just three minutes more than Djokovic to complete his day's work.
Goffin matched his best-ever performance at the majors by reaching his first Wimbledon quarter-final.
The Belgian beat Spain's Fernando Verdasco 7-6 (11/9), 2-6, 6-3, 6-4.
"It's so tough to beat Novak in the best of five and especially here on grass," admitted 28-year-old Goffin.
"Even for Roger, it will probably be the toughest challenge."
Also joining Nadal in the last-eight was his compatriot Roberto Bautista Agut who reached his first Wimbledon quarter-final and second at the majors this year when he defeated France's Benoit Paire 6-3, 7-5, 6-2.
The 31-year-old world number 22 will face either 2016 runner-up Milos Raonic of Canada or Argentina's Guido Pella for a place in the semi-finals.
Paire said he was seriously under-par.
"I have a tear in my abdominal, so I try to serve, like, 60%, 70%, but it's tough," said the Frenchman.
Bautista Agut, who has now defeated Paire seven times in seven meetings, also made the quarter-finals at the Australian Open in January.
He will face Argentine 26th seed Guido Pella who reached his first Grand Slam quarter-final with a come-from-behind 3-6, 4-6, 6-3, 7-6 (7/3), 8-6 win over Canadian 15th seed Milos Raonic.
Pella claimed victory on a fourth match point after surviving a barrage of 33 aces and 80 winners from the 2016 Wimbledon runner-up.
With Federer, Djokovic, Nadal, Querrey and Bautista Agut all winning, there will be five 30-somethings in the last-eight.
Wimbledon results on Monday (x denotes seeding):
Novak Djokovic (SRB x1) bt Ugo Humbert (FRA) 6-3, 6-2, 6-3
David Goffin (BEL x21) bt Fernando Verdasco (ESP) 7-6 (11/9), 2-6, 6-3, 6-4
Guido Pella (ARG x26) bt Milos Raonic (CAN x15) 3-6, 4-6, 6-3, 7-6 (7/3), 8-6
Roberto Bautista Agut (ESP x23) bt Benoit Paire (FRA x28) 6-3, 7-5, 6-
Sam Querrey (USA) bt Tennys Sandgren (USA) 6-4, 6-7 (7/9), 7-6 (7/3), 7-6 (7/5)
Rafael Nadal (ESP x3) bt Joao Sousa (POR) 6-2, 6-2, 6-2
Kei Nishikori (JPN x8) bt Mikhail Kukushkin (KAZ) 6-3, 3-6, 6-3, 6-4
Roger Federer (SUI x2) bt Matteo Berrettini (ITA x17) 6-1, 6-2, 6-2
Alison Riske (USA) bt Ashleigh Barty (AUS x1) 3-6, 6-2, 6-3
Serena Williams (USA x11) bt Carla Suarez Navarro (ESP x30) 6-2, 6-2
Barbora Strycova (CZE) bt Elise Mertens (BEL x21) 4-6, 7-5, 6-2
Johanna Konta (GBR x19) bt Petra Kvitova (CZE x6) 4-6, 6-2, 6-4
Elina Svitolina (UKR x8) bt Petra Martic (CRO x24) 6-4, 6-2
Karolina Muchova (CZE) bt Karolína Pliskova (CZE x3) 4-6, 7-5, 13-11
Simona Halep (ROU x7) bt Cori Gauff (USA) 6-3, 6-3
Zhang Shuai (CHN) bt Dayana Yastremska (UKR) 6-4, 1-6, 6-2
Wimbledon men's singles quarter-finals line up (x denotes seeded player):
Novak Djokovic (SRB x1) v David Goffin (BEL x21)
Guido Pella (ARG x26) v Roberto Bautista Agut (ESP x23)
Sam Querrey (USA) v Rafael Nadal (ESP x3)
Kei Nishikori (JPN x8) v Roger Federer (SUI x2)
Wimbledon women's singles quarter-finals line up (x denotes seeded player):
Alison Riske (USA) v Serena Williams (USA x11)
Barbora Strycova (CZE) v Johanna Konta (GBR x19)
Elina Svitolina (UKR x8) v Karolina Muchova (CZE)
Simona Halep (ROM x7) v Zhang Shuai (CHN)