US Open: Novak Djokovic up and running in bid for historic calendar Grand Slam

World No 1 overcame second set wobble to defeat Danish qualifier Holger Rune

Novak Djokovic needed four sets to get past Holger Rune in the first round of the US Open on Tuesday night. Getty

Novak Djokovic began his bid for an historic calendar Grand Slam by defeating Danish qualifier Holger Rune, and a one-sided crowd, in the first round of the US Open on Tuesday night.

The Serbian world No 1, who has already won the other three majors this season, claimed a 6-1, 6-7, 6-2, 6-1 victory after two hours and 15 minutes in the night feature at Arthur Ashe Stadium.

"It wasn't the best of my performances," Djokovic, 34, said. "At the same time, he played well in the second set when it mattered and I didn't serve well in the second set."

History-chasing Djokovic, who has won eight of the past 12 Grand Slam events, will next face 121st-ranked Dutchman Tallon Griekspoor, a rival the top seed admitted he didn't know much about.

"I know this court well," Djokovic said. "Hopefully that's going to help."

Reigning Australian Open, Roland Garros, and Wimbledon champion Djokovic would complete the first men's singles calendar-year Slam since Rod Laver in 1969 by winning the crown on the New York hardcourts.

He would also break the deadlock for all-time men's Slam titles at 20 which he shares with Roger Federer and Rafael Nadal, both absent due to injuries, as is defending champion Dominic Thiem.

Rune, ranked 145th, began cramping in the third set and struggled to finish.

"From the third or fourth game in the third set, he couldn't move much," Djokovic said. "You could see he struggled a lot. I feel for him."

Djokovic won the first set in 26 minutes without facing a break point, fell behind 3-0 to start the second before battling into the tie-breaker, where Rune grabbed leads of 4-0 and 6-3. After two Djokovic service winners, he sent a backhand service return long to drop the set.

In the third set, Djokovic broke to lead 3-1 and Rune began getting treatments between games, grimacing at times and struggling to run for shots to the end.

Fans chanted "Rune" throughout and applauded the young Dane's bravery as he played on despite being hampered by cramp.

After wrapping up victory Djokovic did not deliver his customary post-match celebration – sharing his heart with all four sides of the court – and he later said he thought the Arthur Ashe Stadium crowd had been booing him.

"I didn't know what they were chanting honestly. I thought they were booing," Djokovic said. "I don't know, it was not ideal atmosphere for me ... But I've been in these particular atmospheres before, so I knew how to handle it.

"It's the largest stadium in sport. Definitely the loudest and the most entertaining stadium we have in our sport ... Obviously you always wish to have crowd behind you, but it's not always possible. That's all I can say."

Earlier Tuesday, Olympic champion Alexander Zverev stretched his win streak to 12 matches and warned he has his eyes on denying Djokovic the Slam.

Fourth seed Zverev, who beat Djokovic in an Olympic semi-final to deny the Serb a shot at an unprecedented golden Grand Slam, dispatched American Sam Querrey 6-4, 7-5, 6-2.

"I hope in two weeks' time I'll be on an 18-match winning streak," said Zverev, who would claim his first Grand Slam title if he creates such a run.

The 24-year-old German, last year's US Open runner-up, hit 18 aces and 40 winners while never facing a break point in advancing after an hour and 40 minutes.

"Novak is chasing history," Zverev said. "But the young guys are going to try and get in the way of that. I'm going to try to give him a challenge as well."

Zverev, who next faces Spain's Albert Ramos-Vinolas, could face Djokovic in the semi-finals.

"I hope I can keep the level up," Zverev said. "To beat Novak here is going to be an extremely difficult task."

In the women's event, world No 1 Ashleigh Barty, coming off wins at Wimbledon and Cincinnati, began her chase for back-to-back major titles by defeating Russian Vera Zvonareva 6-1, 7-6.

"Being able to work my way around that and get through in straight sets was really pleasing," Barty said. "When my back was against the wall late in that buster, I came up with some really good stuff."

The 25-year-old Australian next faces Denmark's Clara Tauson as she goes for her sixth title of the year.