In one of the crucial games, Djokovic repelled two break points at 3-4 and he was awarded in the next game, breaking Roger for a 5-4 lead after a loose backhand from the Swiss.
The victory for Nishikori means that for the first time in the open era there will be a Japanese man and woman contesting the semifinals of a grand slam as Naomi Osaka cruised past Ukraine's Lesia Tsurenko 6-1 6-1.
He added: "I personally have never sweated as much as I have here".
Millman was so sweaty that he had got special permission to change at 2-2 in the second set of his quarterfinal against Djokovic. As play resumed, so did Djokovic's dominance and Millman literally had the air sucked out of him, this time for reasons not the weather. We were all sweating.
As John Millman duckwalked off the court in the middle of his US Open match to change his sopping clothes, Novak Djokovic peeled off his own soaked shirt, laced his hands behind his head and leaned back in his courtside chair with a smile.
"Changing a lot of t-shirts, shorts and just trying to hang in there and find a way to win".
Widely considered the best returner in the game, Djokovic kept accumulating chances - and then failing to cash them in.
The Serbian won only four of 20 break points against an opponent whose surprise run has been one of the stories of the tournament. But up 3-2, he received two time violations and Millman broke back for a 4-3 lead. After missing several open shots, Djokovic doubled over and staggered around the court as his camp - coaches, trainer, and wife Jelena - looked on worriedly.
It was a sad comedown for the unheralded Aussie, who put in the shift of a lifetime on Tuesday to oust the five-time victor with a four-set victory.
Djokovic said the tournament needs to address the problem of air-conditioning in an arena which can hold nearly 25,000 people.
Nishikori is appearing in his third Grand Slam semi-final of his career, all of which have come in NY.
Suarez celebrated her 30th birthday with a victory over five-time Grand Slam victor Maria Sharapova on Monday. That was at Wimbledon in 1995, and both Shuzo Matsuoka and Kimiko Date lost in that round.
Seeded seventh, Cilic has reached two Grand Slam finals in the past 18 months, falling to Roger Federer in the final of the Australian Open in January. Because whether it's night or day, we just don't have air down there.
Marin Cilic, of Croatia, argues with the chair umpire during a match against Kei Nishikori, of Japan, in the quarterfinals of the U.S. Open tennis tournament, Wednesday, Sept. 5, 2018, in NY.
The momentum swung throughout the match with 2014 champion Cilic looking in control when leading 4-2 in the second set before losing six games in a row.
Deep in the second set, Djokovic, the Serb with perhaps the strongest return game in history, had failed to convert 13 consecutive break points.
The No. 21 seed continued his strong season after returning from a wrist injury that forced him to miss the U.S. Open a year ago and will play No. 6 seed Novak Djokovic on Friday.