The second set was a struggle for both players in the humid conditions, Djokovic at times struggling with cramp, while Millman was granted permission to leave the court for fresh gear as he continued to sweat profusely.
Each of the Japanese's three Grand Slam semifinal appearances have come in NY and he exorcised some of the demons still lingering from his 2014 final heartbreak in Arthur Ashe Stadium by disposing of his attacker from that early September evening four years ago.
Osaka was an easy victor in her quarterfinal, eliminating unseeded Lesia Tsurenko of Ukraine 6-1, 6-1 in all of 57 minutes.
The 20-year-old said she was nervous, claiming to be "freaking out inside" - though it certainly never showed.
In the match before Nishikori's, Naomi Osaka moved into her first Grand Slam semifinal by routing Lesia Tsurenko 6-1, 6-1.
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Asked why he feels he boasts such a strong record against Nishikori, Djokovic said: 'I mean, I have a very good head-to-head score against him.
Tsurenko didn't appear bothered by the conditions, but whether it was her health or just first-time jitters, she was off from the minute she stepped onto the court at Arthur Ashe Stadium. The bottom half of the draw also had former champion Marin Cilic and, therefore, Nishikori was an unforeseen player in the semi-finals, unlike the top half of the draw, where Rafael Nadal will be playing the World no. 3 Del Potro, according to predictions.
And as against Federer, that was enough to lose the first set after Djokovic benefited from a lucky net chord and then fought off a break point in the final game to serve the set out.
Earlier, Nishikori defeated the man he lost to in the final four years ago, Marin Cilic 2-6 6-4 7-6 (5) 4-6 6-4.
But after reaching the final in Monte Carlo, the French Open fourth round and the Wimbledon quarter-finals, Nishikori believes an elusive first grand slam is within reach.
"I hate matches like this", Tsurenko said.
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And when he consolidated for 4-1 the match seemed as if it was heading in only one direction, especially as he carved out a break point opportunity for a double break of serve.
This night was cooler, as the temperature dipped, but the humidity was above 80 percent, so with Millman drenched, he sought permission for a wardrobe change at 2-2 in the second set. "I tried to swing a little more, play aggressive and start working better from 4-2 down", he added.
He said: "He's got one of the best two-handed backhands in the game and very quick".
"It was just one of those nights, I guess, I felt I couldn't get air. So it came down to a couple points". Novak won just two points more than Roger and he had to dig deep in his service games to emerge as a victor before the deciding set, saving 19 out of 23 break points and stealing Federer's serve six times from 13 opportunities. After the first, he double-faulted, and he wound up getting broken there.
But Djokovic broke back in the match's next-to-last game, then served out the victory at love.
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