Djokovic spent a lot of time on the sidelines recovering from a terrible elbow injury that had many fans worrying that he may never return to his scintillating best.
When Anderson broke again in the fourth, Federer was suddenly on the ropes. "Do you think I ruined the court?" he bellowed at Ramos.
"Today I had a tough opponent, a big challenge", said Djokovic. "I just had to go back to basics and hit as many balls as I can on the practice courts, just get that feel".
A fuming Novak Djokovic accused the chair umpire of "double standards" before advancing to his first Wimbledon semi-final in three years with a four-set dispatch of Kei Nishikori. "I mean, anybody who saw the match, I mean, saw that literally I kind of touched the grass", Djokovic said.
"I'm very pleased", Djokovic said after the victory.
"He was playing very deep, he was going both sides with his back and then his forehand too. he was making me run all the time". I think that's not fair.
Djokovic was able to regain his composure, though, and managed to win by four sets to one.
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The Serbian won 6-3, 3-6, 6-2, 6-2 on Centre Court to set up a meeting with either Rafael Nadal or Juan Martin Del Potro in the semi-finals on Friday.
Novak Djokovic made a right racket at Wimbledon.
"I like the level of tennis that I'm playing on right now", Djokovic said.
But the 12-times major victor regained his cool sufficiently enough to safely take his place in the semi-finals for the first time since snaring his third title at The All England Club in 2015.
Seeded 12, Wednesday will Djokovic's 41st appearance in a Grand Slam quarter-final.
Anderson added that Federer, who won his first Wimbledon title in 2003, is the flawless role model for the sport - and for those players in the chasing pack. It was the first time he played a fourth set at Wimbledon since 2016 against Milos Raonic.
It was on Djokovic's serve and 0-40 down, he slowed things up, taking on average 29 seconds to serve, and saved all three break points before closing out the game.
For the only the second time at Wimbledon, Federer was beaten after holding a two-set lead, with his previous loss from that position coming against Jo-Wilfried Tsonga in the 2011 quarterfinals. If there were obvious empty seats for the lunchtime encounter, with defending champion Roger Federer in action at the same time on Court One, the entertainment could not be faulted.