Novak Djokovic set up a semi-final blockbuster against Carlos Alcaraz at the US Open as he kept his dreams of a 25th grand slam title alive.

Djokovic overcame Taylor Fritz and a rowdy New York crowd, quelling the American’s fightback to end hopes of a home men’s champion for another year.

Fritz had hoped to finally secure a first victory over Djokovic at the 11th time of asking but the majority of the big moments went the way of the Serbian, who triumphed 6-3 7-5 3-6 6-4 after three hours and 24 minutes.

Djokovic was bothered on numerous occasions by noise from the crowd while he was serving, putting his finger to his lips and blowing ironic kisses after winning the second set.

In the third he remonstrated with umpire Damien Dumusois and Fritz threatened to take the contest to a fifth set, but ultimately Djokovic had the answers.

“It was an incredibly close match, really anybody’s match,” he said. “I thought I was lucky to save some crucial break points in the second and third sets. In these matches a few points decide the win.

“Tough for Taylor to finish on a double fault, he didn’t deserve that. In many of my service games I was just trying to stay alive. I’m really proud of the fight that I put in. I wear my heart on my sleeve always.”

Now Djokovic must try to make it beyond the last four for the first time at a grand slam this year in what will be his 53rd grand slam semi-final.

With victory over Fritz, the 38-year-old tied Jimmy Connors’s record by reaching a 14th semi-final here, also becoming the oldest man through to this stage since the American in 1991.

Djokovic, who had wanted a win as an eighth birthday present for his daughter Tara back home, has played himself into form through the tournament after a shaky start and he was immediately in the ascendancy here, moving into a 3-0 lead.

The match came to life in the ninth game with Djokovic serving for the set, the seventh seed saving five break points before eventually converting his second chance, raising his fist in celebration.

The chances kept coming for Fritz in the early stages of the second but he could not take them and, as the American’s frustration peaked, Djokovic struck to move 4-3 ahead.

But serving for the set he was again unconvincing and on his 11th break point Fritz finally converted only to play a dreadful service game at 5-5 and give the advantage straight back.

At two sets up, Djokovic seemed to have one foot in the semi-finals but, spurred on by the crowd, Fritz kept pushing.

Noise from fans between Djokovic’s first and second serve came to a head in the fourth game of the third set, and it rattled the Serbian, who was broken for the second time.

Djokovic shook his head and gestured for the crowd to be quiet, but the noise only ramped up as Fritz won the third set.

Strong serving from both men kept the fourth level until the 10th game, when Djokovic applied intense pressure on the Fritz serve. The fourth seed, who reached his first grand slam final here last year, saved two match points in epic rallies but double-faulted on the third.

Djokovic leads his head-to-head 5-3 against Alcaraz, who he beat at the Australian Open, but he will go into the match as second favourite given the form here of the young Spaniard.

Alcaraz continued his march through the draw with a 6-4 6-2 6-4 victory over 20th seed Jiri Lehecka, who beat him in Doha earlier this season but got nowhere near on Arthur Ashe.

“I think that today I met the grand slam version of Carlos,” said the Czech. “We played very good rallies but unfortunately he was everywhere. He always managed to do something special.”

Alcaraz is yet to drop a set during the tournament and this match again saw him pull off the sort of apparently impossible shots that he loves as much as the crowd.

A forehand winner down the line played while he was moving backwards into the backhand corner drew a long admiring glance, while Alcaraz put his finger to his ear after winning a key point in the second set with a lunging drop volley.

He did not face a break point in the match and wrapped up victory inside two hours.

On Lehecka’s admiration, he said: “It feels great hearing those words from my opponent today. I think today I just played an almost perfect match.

“So, playing a quarter-final of a grand slam, I’m feeling that way. It seems like, OK, just two more steps to do, and let’s see what happens. I’m just feeling great and hungry to make it.”