It will be Djokovic's 41st appearance in a Grand Slam quarter-final and he will start favourite against Nishikori, who will be in his first last-eight at the All England Club.
"I think Rafa and Del Potro had to be on Centre Court", Murray told BBC.
Either Rafael Nadal or Juan Martin del Potro will provide the next hurdle on Friday. 'Against Anderson he has won all four matches and never dropped a set, so I expect him to comfortably get through.
Nishikori promptly broke serve and then held to go 4-1 up before levelling the match at 1-1 but any sense of a fightback, and the possibility of a first Japanese man in the Wimbledon semi-finals since 1933, was short-lived.
He looks very fired-up, he looks very motivated so I think Novak has got a great shot as well.' Analyzing how elbow issues influenced Djokovic's mental status, Murray added: 'He's spoken about that, he said the mental side has been hard for him. I feel like a lot of aspects of my game can give him a lot of trouble'.
Djokovic saved three break points in the fifth game of the third and made the Japanese star pay by breaking for 4-2 and an eventual two sets to one lead.
It didn't show in Djokovic's play, though, as he embarked upon another swing of four games in succession, holding Nishikori to three points in his next two service sets as he soared into a 4-1 lead.
"Do you think I ruined the court?" he bellowed at Ramos.
The semi-final will be the 32nd of Djokovic's Grand Slam career but he has had to fight to get there.
Khachanov overcame more misfortune as he held to level the third set at 2-2 despite Djokovic twice receiving the help of a net cord, but he could not survive more pressure two games later, scooping a backhand long to put his opponent on the brink.
Del Potro said: 'I think I will be in good condition. Then a combination of fitness, form and family issues made the 12-time grand slam champion all too fallible.
"I felt like it was getting better and better as time went on". I'm going to play semifinals back there again.