(Photo credit: Robert Deutsch-Imagn Images)

Novak Djokovic was in a dancing mood after advancing to the semifinals of the U.S. Open with a 6-3, 7-5, 3-6, 6-4 win over Taylor Fritz on Tuesday night in New York.

The win ended shortly before midnight on the day Djokovic's daughter turned 8 years old. In her honor, the 38-year-old Serbian busted out some 'Kpop Demon Hunters' dance moves after sealing the victory.

Djokovic, the event's seventh seed, lost in the semifinals of each of the year's previous three Grand Slam events. He is still searching for a 25th career major singles title that would put him above Margaret Court for the all-time record among men and women.

The path only gets tougher, though, as Djokovic will oppose No. 2 Carlos Alcaraz in the semifinals on Friday. The 22-year-old Spaniard extended his indomitable run by defeating No. 20 seed Jiri Lehecka of the Czech Republic 6-4, 6-2, 6-4 in a shade less than two hours.

Djokovic wrapped up his win by recording the lone break of the fourth set in the final game. He needed three match points, with Fritz double-faulting on the last one to end it.

'It was an incredibly close match,' Djokovic said. 'It was really anybody's match. ... For most of the second and third set, he was the better player. And in these kind of matches, a few points decide the winner. It was fortunately coming on my side, particularly at the end of the fourth.

'That last game was nerve-wracking, honestly. Tough one for Taylor to finish with a double fault. He didn't deserve that. But great fight and great tournament from him for sure.'

Djokovic next will look to improve on his 5-3 head-to-head record vs. Alcaraz. Djokovic won each of their past two meetings, in the Paris Olympics final last summer and in the quarterfinals of the Australian Open this year.

Fritz's defeat means another year has passed without a U.S. player winning a major men's singles title. Andy Roddick's 2003 U.S. Open title remains the last Grand Slam win by an American.

Alcaraz won his 11th straight match and reached his ninth Grand Slam semifinal -- including his third in a row, following his victory at the French Open and loss in the Wimbledon final.

Alcaraz once again controlled a match through his serve. Not only did he win 38 of 45 first-service points (84.4 percent), he did not drop a service game, going 14-for-14.

Through five matches at Flushing Meadows, Alcaraz has lost a grand total of one service game -- winning 68 of 69.

Lehecka was his highest-seeded opponent so far, but that will change when Alcaraz opposes Djokovic in the semifinals.

Alcaraz, who won the Cincinnati Open last month when Italian star Jannik Sinner retired early in the final, can overtake Sinner for World No. 1 this week. Alcaraz will ascend to No. 1 if he matches or exceeds Sinner's finish this week.

'If I think about the No. 1 spot too much, I'm going to put pressure on myself, and I just don't want to do that,' Alcaraz said. 'I just want to step on court, try to do my things, follow my goals and try to enjoy as much as I can. The No. 1 (spot) is there, but I try to not think about it too much.'

Sinner's quarterfinal match is slated for Wednesday against fellow Italian and No. 10 seed Lorenzo Musetti.

During the second set Tuesday, Alcaraz converted an improbable drop volley with his back to the net and also countered Lehecka's would-be smash winner with a perfect backhand down the far line. He was asked in his on-court interview if he's known for playing back his own highlight reels.

'I'm not, but sometimes when I go to the living room, my little brothers are watching my highlights, so I just sit down and watch them,' Alcaraz said with a grin.

--Field Level Media