Said an emotional Osaka after her hard-fought victory, "I wouldn't forgive myself if I managed to lose that".
Nishikori raced into a 4-1 lead but Cilic broke back to take the set to 4-4.
Osaka represents Japan and was born in Tokyo to a Japanese mother and Haitian father, but the family moved to NY when she was three before relocating to Florida five years later.
Once she did, the 20-year-old Osaka found they had plenty in common.
To get to Saturday's championship match, 20th seed Osaka will have to get past U.S. 14th seed Madison Keys who breezed past Spain's Carla Suarez Navarro 6-4, 6-3.
"You survive on the court then thrive with a win", said Djokovic, who converted just four of his 20 break points and made 53 unforced errors before he was finally able to accomplish what Federer couldn't in seeing off Millman.
Only once had Japan had a man and woman reach the quarterfinals of the same major, and Shuzo Matsuoka and Kimiko Date both lost in that round at Wimbledon in 1995.
When Nishikori became the first Asian male to reach a Grand Slam singles final four years ago, hundreds of fans packed into a convention hall to cheer him on at a standing-room-only public viewing event in his hometown of Matsue. "It would be really cool".
But after labouring through the heat in her previous match, Tsurenko said she was sick Wednesday, waking up with a sore throat and not breathing well.
"Today was not my day, obviously", Tsurenko said.
Tsurenko laboured in the heat during her fourth-round victory over Marketa Vondrousova, having her temperature and blood checked during a medical timeout in the first set and almost quitting when she trailed early in the second.
Osaka had consecutive 50-minute matches earlier in the tournament, including a 6-0, 6-0 thrashing of Aliaksandra Sasnovich in the third round.
"I really, really, really hope she makes it to the final here and I hope that we do, too".
In the end she made it easy, swatting aside unseeded Ukrainian Lesia Tsurenko in under an hour, 6-1 6-1. So far in this Open, she's held opponents scoreless in three sets, and she's dropped only one set thus far.
It was another hot afternoon Wednesday, with temperatures in the high-80s (30s Celsius) but feeling some 10 degrees hotter with the humidity.
There was a subdued atmosphere on Arthur Ashe Stadium with the crowd struggling to get into the match.
"I hate matches like this", said Tsurenko. It was odd enough to see a player be allowed to do that during, instead of after, a set, but even odder for it to happen after an even number of games, rather than at an odd-game changeover.