NEW YORK -- Novak Djokovic put aside all of it, from his opponent's unheard-of, middle-of-a-set chance to change out of sweat-soaked clothes and shoes to consecutive time violations because Djokovic let the serve clock expire to the 16 break points he wasted.
Djokovic moved a step closer to a third championship at Flushing Meadows and a 14th Grand Slam title overall by eliminating Millman 6-3, 6-4, 6-4 on Wednesday to get to the tournament's semifinals for an 11th appearance in a row. He sat out last year because of an injured right elbow.
The No. 6-seeded Djokovic, who won Wimbledon in July, had been drawn to face Federer in the quarterfinals. But Millman scuttled that showdown by stunning the 20-time Grand Slam champ in four sets in the fourth round on a hot and humid evening that Federer said sapped his energy and made it hard to breathe.
"I was, alongside many other people, anticipating the match against Federer,'' Djokovic said.
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. 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.
"I was struggling. He was struggling. We were all sweating. Changing a lot of T-shirts, shorts,'' said Djokovic, who will face 2014 US Open runner-up Kei Nishikori on Friday. "Just trying to find a way to hang in there.''
When Millman apologized for leaving the court at that juncture, Djokovic replied, "I'm fine to have a little rest,'' then sat down on his sideline bench without a shirt on and cooled off.
Widely considered the best returner in the game, Djokovic kept accumulating chances and then failing to cash them in. He was able to come through on only four of his 20 break points.
There were other issues for Djokovic, as well, including in the third set when, ahead by a break, he was called by the chair umpire for allowing the 25-second serve clock -- making its Grand Slam debut at this tournament -- to run out on back-to-back points. After the first, Djokovic 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.
"I think the guy's beat a brick wall once,'' Millman said, "because he makes you work hard for every point, and it's relentless.''
Earlier Wednesday, Nishikori defeated the man he lost to in the US Open final four years ago, Marin Cilic, 2-6, 6-4, 7-6 (5), 4-6, 6-4. Add that to No. 20 Naomi Osaka's 6-1, 6-1 win over unseeded Lesia Tsurenko of Ukraine, and Osaka and Nishikori give Japan semifinalists in both men's and women's singles at the same Grand Slam tournament for the first time in tennis history.
"It's great to see,'' said Nishikori, who is into his third major semifinal -- all in New York -- but is still in search of his first Grand Slam trophy.
Only once in the professional era that began in 1968 had Japan had a men's and women's player in the quarterfinals at the same tournament. That was at Wimbledon in 1995, and both Shuzo Matsuoka and Kimiko Date lost in that round.
The seventh-seeded Cilic won the 2014 final in straight sets for his only career major title. Nishikori said this week that he was nervous once that championship match began, but Wednesday's match was nothing like that day.
Instead, it resembled their 2010 second-round match at Flushing Meadows, when Nishikori rallied to win in five sets in 4 hours, 59 minutes, the fifth-longest men's singles match by time in US Open history.
Each man blew chances to gain control Wednesday and perhaps have a much quicker ending to a match that had wild swings of momentum.
Cilic appeared to be coasting after taking the first set and opening a 4-2 lead in the second. The Croatian then had the lead in the third-set tiebreaker, until double-faulting on consecutive serves.
After Cilic evened the match by taking the fourth following a 10-minute break for heat, Nishikori was on the verge of running away with the fifth, holding a break point for a 5-1 lead. Instead, Cilic held and then broke Nishikori on his way to evening the set at 4-all; but then Nishikori took the final two games.
The No. 21-seeded Nishikori continued his strong season after returning from a wrist injury that forced him to miss the US Open last year. He faces Djokovic next.
"I wish I don't go to five sets every time,'' Nishikori said.
The Associated Press contributed to this report.