Murray, seeded second, led by two sets to one but eventually lost 1-6 6-4 4-6 6-1 7-5 in three hours 57 minutes.
The Wimbledon champion lost his rhythm after rain brought the roof across, and his cool when the stadium sound system interrupted a break point.
Sixth seed Nishikori goes on to face Juan Martin del Potro or Stan Wawrinka.
“It was too exciting on the court, but I tried to stay calm,” said Nishikori, the 2014 runner-up in New York.
“In the beginning I didn’t start well – he has a great return – but I finished well. The rain delay helped me to change tactics. I tried to hit a few more drop-shots than usual today and it worked really well.”
Murray, 29, had been on course to become only the fourth man since the Open era began in 1968 to reach all four major finals in the same year, having finished runner-up at the Australian and French Opens, and won Wimbledon.
The decision to keep the roof closed, despite the weather quickly improving, and a “malfunctioning digital audio sound processor” – as described by the United States Tennis Association – upset Murray’s rhythm and composure, in contrast to the impressive Nishikori.
Murray began in terrific form, overpowering Nishikori in a 35-minute first set, but lost control of the match when a passing rain shower led to the new roof being brought over Arthur Ashe Stadium.
Nishikori levelled at one set all and infuriated Murray by breaking straight back three times after losing his serve.
Murray’s frustration only grew when he let a 40-0 lead slip at 4-4 in the third, but when the Scot took the next two games he looked to have finally taken control.
His momentum stalled dramatically early in the fourth set when he was seemingly in charge of a rally on break point, only for the stadium sound system to emit a loud noise that caused the umpire to halt the point.
Murray was furious, arguing with both umpire and tournament referee, but the point, the game and, within half an hour, the set went Nishikori’s way, reports the BBC.
A butterfly persistently fluttering around the net only added to Murray’s annoyance as the 2012 champion lost seven straight games, but twice fought back from a break down in the fifth set to edge ahead at 5-4.
With 16 service breaks between them, there seemed every chance Murray would finally get over the finish line, but Nishikori played superbly to hold to love and it was the Japanese who then claimed the 17th and decisive break.
There was to be no final set tie-break as Nishikori proved the stronger with another nerveless hold that ended Murray’s hopes.
Meanwhile, World No 1 Serena Williams fended off spirited Simona Halep on Wednesday, downing the fifth-seeded Romanian 6-2, 4-6, 6-3 to reach the US Open semifinals.
Williams, seeking a record seventh US Open title and 23rd Grand Slam crown, fired 18 aces en route to the triumph, which set up a Thursday evening meeting with first-time Grand Slam semi-finalist Karolina Pliskova for a place in Saturday’s championship match.
But she made her task against 2014 French Open finalist Halep harder with 43 unforced errors and Halep, firing on all cylinders from the baseline took advantage.
The Romanian became the first player in the tournament to break Williams’s serve, and the first to take a set off the top seed.
After failing to convert any of a dozen break points in the 65-minute second set, Williams regained control in the third with a break for 3-1 and steamed home from there.
Williams’s semi-final against Pliskova promises more fireworks. The 10th-seeded Czech leads the WTA tour in aces this year.
After surviving a match point en route to a fourth-round victory over Venus Williams, Pliskova beat 18-year-old Croatian Ana Konjuh 6-2, 6-2.
Despite her dearth of Grand Slam success, Pliskova is playing with confidence after winning her biggest title to date on the hard courts of Cincinnati.
She beat Angelique Kerber in the final to deny the German world No 2’s bid to supplant Serena atop the world rankings.
Serena said she hadn’t talked to her sister yet about how best to approach Pliskova.
“I haven’t even gotten that far yet, actually,” she said. “I’m still trying to just get over this match. I’m sure Venus will tell me something, but I’ll be there. I’ll be ready tomorrow.”
Kerber, who booked her semifinal slot on Tuesday with a 7-5, 6-0 victory over 2015 finalist Roberta Vinci, can still nudge Serena from the summit.
No matter the outcome of Kerber’s semifinal clash with former world No 1 Caroline Wozniacki, Serena must now reach the final to stretch her reign to a record-breaking 187 weeks.
If Kerber advances to the title match, Serena will have to beat her for a seventh US Open trophy to stay No 1.
