That dented the Japanese confidence and Djokovic grabbed the double break to seal set three but the inexorable march to victory that many had predicted did not materialize.
The 24th-seeded Nishikori was able to attack Djokovic's second serve and had a chance to take the lead when he was 0-40 up at 2-2 in the third set.
A tight third set turned in Djokovic's favour as Nishikori went wide and that was enough for the fired-up three-time champion to edge back in front as he served into a 2-1 lead.
"I thought it was unnecessary to get the warning", he told the BBC after the 6-3 3-6 6-2 6-2 win.
Isner's 41 attempts at reaching a first Grand Slam semi-final is the second-most in the Open era after fellow American Sam Querrey, who made the Wimbledon last four in 2017 on his 42nd try.
When Del Potro sent a forehand rifling down the line to take the third set, it seemed Nadal might be following Federer out of the tournament, but the World No.1 recovered superbly to triumph 7-5 6-7 (7/9) 4-6 6-4 6-4 and keep alive his hopes of an 18th Grand Slam title. "I'm a different person, different player today". Djokovic is a national hero and I thank him for it, but how can you support Croatia, how don't you feel ashamed? 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. I think that these performances here at Wimbledon have been the best I've had in the last 12 months.
Those fears dimmed when Nishikori broke Nole in the opening game of the fourth set, but again the balance tipped in the Serb's direction when he broke back in the follower.
Khachanov's display was flashy but full of errors, and Djokovic was ruthless in punishing them, coming through 6-4 6-2 6-2 to set up a last-eight meeting with Kei Nishikori. "He's one of the best players on the tour".
Explaining the process which he underwent to get back closer to his best, 31-year-old Djokovic added: "I was putting a lot of hours on the practice courts and really being dedicated and motivated to get back on that level that I'm used to playing and have played over the years".