The victory for Nishikori means that for the first time in the open era there will be a Japanese man and woman contesting the semifinals of a grand slam as Naomi Osaka cruised past Ukraine's Lesia Tsurenko 6-1 6-1.
Djokovic, who was won all 11 of the quarter-finals he has played here, beat Millman 6-3, 6-4, 6-4 in two hours and 48 minutes on another sweltering night in Arthur Ashe Stadium.
Forty-eight hours after the 37-yearold Swiss suffered one of the most shocking defeats of his career when he was beaten by John Millman, Djokovic swept aside the Australian on Wednesday to secure his place in the semi-finals of the US Open.
"If not "the" quickest, then one of the quickest players on the tour".
It was first played at the U.S. Open in 2005, but did not have a match in Arthur Ashe Stadium until a year ago.
The US Open is not available to watch on TV for United Kingdom viewers.
"There are so many people that stayed at the stadium and its past midnight".
American David Wagner, the top-ranked quad player in the world, is attempting to win his fourth U.S. Open quad singles title and his ninth in doubles. We've witnessed throughout our rivalries in 10, 15 years, there are periods and intervals where I win couple matches in a row, then they win couple matches in a row. But Kei woke up and found his form and reeled off six straight games to take the second and go up in the third with a break.
Osaka becomes the first Japanese woman in a Grand Slam semifinal since Kimiko Date at Wimbledon in 1996. Serving for the set, Djokovic saved an additional two break points, forcing an error from Roger to close the set 6-4 and move a set away from the title (Federer was three from 17 on break points at that moment). She recovered to win in three sets, with her opponent accusing her of acting after the match.
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The Serb, a two-time champion, faces American Tennys Sandgren, while 2006 victor Sharapova plays Sorana Cirstea. Kyrgios reached the third round by seeing off France's Pierre-Hugues Herbert 4-6, 7-6 (8/6), 6-3, 6-0.
It's another scorching hot day in NY and that means the extreme heat policy is back in effect for the third consecutive day at the U.S. Open. The third set Nishikori won the tiebreak but in the fourth game Cilic served well and naturally equalized.
The policy is a rule on the women's tour, but not the men's. But, you know, I think that with so many players retiring that first round, first day or second day, and so many players struggling to breathe, especially on the center court, which, you know, doesn't, there is no circulation of the air at all, especially court level.
The win meant that Djokovic advanced to his 11th straight USA semifinal - a streak only bettered by Jimmy Connors.
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.
Djokovic won his 13th Grand Slam at Wimbledon, just after beating Millman 6-2, 6-1 at Queen's Club in their only previous meeting.
Amazon have exclusive rights to the final major of the year after outbidding Sky.
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.
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