Millman, though, also leaves Flushing Meadows a victor and with renewed belief that he can challenge for major spoils following his stirring run to the second week of a grand slam for the first time.
"I'm really, really proud - not proud but happy - with how my body has held in there and physically I actually feel pretty good in this caper", Millman said.
Djokovic used the break to send a ballboy over to his box in the stands seeking to get some tablets he said his wife had brought to the tournament for him but which had somehow not made it into the bag he took on court.
Djokovic broke early to take a 3-1 leave in the third set but a lapse in concentration allowed Millman to draw level.
Roger Federer said he felt like he "couldn't get air" when suffering a shock defeat to Millman on Monday and Djokovic expressed similar views after beating the Australian two nights later. Djokovic said the conditions at this year's tournament were the toughest he had known in the last 10 years.
The Serb, twice champion at Flushing Meadows, has now won all 11 of his quarter-final matches in NY.
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No U.S. man has won the singles title in NY since Andy Roddick in 2003, and none has even reached the semifinals since Roddick in 2006.
Deep in the second set, Djokovic, the Serb with perhaps the strongest return game in history, had failed to convert 13 consecutive break points.
This one wasn't exactly simple for Djokovic: He only converted four of 20 break points.
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.
Djokovic who missed last year's edition due to an elbow injury will slug it out with Japan's Kei Nishikori in the last four on Friday. Millman saved five break points, even survived two straight double-faults.
She'll face No. 14 Madison Keys of the US on Thursday night.
Osaka celebrated her win calmly and coolly unlike the floods of tears which greeted her last-16 victory over Aryna Sabalenka. She's also the first Japanese woman to make the US Open semifinals in 22 years.
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The Serb said that the trying conditions had made the match hard for both players.
Naomi Osaka, of Japan, reacts after defeating Lesia Tsurenko, of Ukraine, during the quarterfinals of the U.S. Open tennis tournament, Wednesday, Sept. 5, 2018, in NY. I think she can win the title now.
Although Djokovic won the first three games, the rallies were hard-fought from the start as Millman kept making his opponent hit the extra ball.
Millman, his clothes soaked, made the unorthodox request to go change after the fourth game of the second set - Djokovic agreeing.
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.
Keys punched her ticket with a victory over Carla Suarez Navarro on Wednesday.
Nadal advances to US Open semi-final
Remarkably, Thiem was the first top-20 player Nadal has faced at Flushing Meadows since his final win over Novak Djokovic in 2013. The win was sealed when Thiem missed a hard overhead smash long, and Nadal looked to the sky, equal parts overjoyed and relieved.