Novak Djokovic took a first unsteady step towards completing the calendar-year Grand Slam on Tuesday as the Serb laboured into the second round of the US Open with a 6-1 6-7(5) 6-2 6-1 win over dashing Danish teenager Holger Rune.

On paper, the contest was a total mismatch - an 18-year-old qualifier making his Grand Slam debut against a player chasing a 21st major title.

While the outcome was exactly what was expected, the effort needed by Djokovic to see off the fearless Dane, who battled to the end despite suffering cramp, was not.

"I started great. Played a really, really good first set," said Djokovic. "After that, I don't know, I was 4-3 serving in the second set, everything was working well, but then I just lost the first serve.

"I had until tonight tons of experience playing on this court, for him it was the first one.

"Still you get nerves. You still are feeling a little bit rusty at the beginning."

The match got underway amid a somewhat flat atmosphere inside Arthur Ashe Stadium but the crowd were chanting the little-known Dane's name after he stunned Djokovic to win the second set.

Aside from that, it was a controlled effort from the 34-year-old Djokovic, far different from the Serb's last match on Arthur Ashe Stadium court which ended with him being disqualified after swatting a ball in frustration that struck a line judge.

'CRAZY EXPERIENCE'

The stone-faced world number one was all business from the start, breaking his opponent at the first opportunity and rolling through the set in just 26 minutes. Playing his first event since a disappointing Tokyo Olympics there were signs of rust and a lack of intensity, particularly in a sloppy second set when Rune broke him twice and forced the set to tie-break that he easily won.

But there was never any panic from Djokovic, who turned up the pressure in the third with an early break to regain control as Rune began to suffer cramp.

As Rune grimaced with every step, Djokovic showed his ruthless side, moving the youngster from line-to-line and taking the set 6-2. Rune was determined to battle his way to the end but a Djokovic victory was now certain and the Serb wrapped up the match by taking the fourth set 6-1.

"It was a crazy experience, playing against Novak on Arthur Ashe is probably one of the dream come true," said Rune.

"To be able to win one set as well was great."

The Dane said his fitness struggles made winning "impossible".

"I had high belief in myself throughout the whole match," he added.

"Unfortunately my fitness let me down.

"I started cramping already in the beginning of the third set.

"I knew if I had to win, I really had to fight for every point but with my body at this point, it was impossible."