Naomi Osaka won her quarterfinal in the match that preceded Nishikori's. Millman fought back to take a 4-3 lead before Djokovic finished him off by winning the final two points of the game.
Djokovic, the victor in 2011 and 2015, faces Kei Nishikori in Friday's semi-finals, his 11th successive appearance in the last-four.
"It's great to see", said Nishikori, who is into his third major semifinal - all in NY - but is still in search of his initial Slam trophy.
Osaka was an easy victor in her quarterfinal, eliminating unseeded Lesia Tsurenko of Ukraine 6-1, 6-1 in all of 57 minutes.
Osaka, who is just 20 years old, is having a terrific 2018 season.
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.
"I've gotten a lot better managing my emotions once it gets to this part and knowing that everything is going to be probably more amped up", Keys said.
"When I was 18 years old, I had two dreams", said the 38-year-old Italian.
McEnroe and co-commentators Chris Fowler and Brad Gilbert continued to toe the line between respect and praise throughout the first set.
She also played the longest Grand Slam match for a woman that year, overcoming six match points to beat Svetlana Kuznetsova 6-4, 1-6, 16-14 in 4 hours, 44 minutes in the fourth round of the Australian Open.
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Having recovered from 3-1 down to lead 4-3 in the breaker, Cilic double-faulted twice in succession and another missed first serve proved costly at set point down as Nishikori pounced on the second delivery with a backhand return victor.
"But once you win more than a match against your top rival, you start to feel like you have maybe a little bit of a mental advantage", added Djokovic, who's looking to get to his 11 semifinal in Flushing Meadows.
Osaka, who was born in Japan but moved to the U.S.at age 3, was followed at Arthur Ashe Stadium by Kei Nishikori, who beat Marin Cilic in a men's quarterfinal. I'd play in a swimming pool if I got to play a quarter-final every week at a Grand Slam.
"I'm also happy for myself, too, being injured a year ago, I couldn't play this tournament".
"From that point on, I felt the match was quite even", he went on.
This night was cooler, as the temperature dipped into the 70s, but the humidity was above 80 percent, so with Millman drenched, he sought permission for a wardrobe change at 2-all in the second set. "Just trying to hang in there, trying to find a way to win the match. So it came down to a couple points".
But he broke back in the match's next-to-last game, then served out the victory at love.
"Especially after coming from injury", he said, "I think I'm enjoying this challenge".
Cilic, who won their final meeting in straight sets, was pushed to the limit this time around with Nishikori extending his dominance to nine wins from 15 meetings.