Novak Djokovic continued his pursuit of a calendar Grand Slam by reaching the US Open third round with a straight-set win over Dutch rival Tallon Griekspoor.

Djokovic, aiming to become only the sixth player to complete a clean sweep of the Australian Open, French Open, Wimbledon and US Open, won 6-2 6-3 6-2.

It was a solid display but the top seed was ruffled by a heckler at one point.

Alexander Zverev, among those expected to challenge the Serb, advanced with a rapid win over Albert Ramos-Vinolas.

In the quickest completed men's singles match so far, 24-year-old fourth seed Zverev needed just one hour and 14 minutes to win 6-1 6-0 6-3 against the Spaniard and reach the third round.

While Djokovic could not match that speed, it was a similarly dominant performance from the 20-time Grand Slam champion against 121st-ranked Griekspoor.

Djokovic, 34, showed signs of rustiness in his opening win over Danish teenager Holger Rune but was much improved in a solid performance on Arthur Ashe Stadium.

In fact, it was a spectator in the crowd who bothered the world number one as much as his opponent.

Leading 4-2 in the second set, Djokovic was disturbed by a shout as he lined up a smash at 30-30 and missing the overhead contributed to the three-time champion dropping his serve.

The Serb channelled his annoyance into an instant break in the next game, but implored the umpire to tell the offender to "shut up" at the beginning of the third set.

"I don't mind he screams between the points, I don't mind that. But he's doing it every second point, during the point, just before I hit it," Djokovic said.

There were no further flashpoints as Djokovic broke twice more in the final set to tee up a third-round meeting with Japan's Kei Nishikori.

Nishikori, runner-up in 2014, won 7-6 (7-3) 6-3 6-7 (5-7) 2-6 6-3 against American Mackenzie McDonald to extend his remarkable winning record in deciding fifth sets to 27-7.

But his record against Djokovic is less impressive, having lost 17 of their 19 meetings and not beating the Serb since their US Open semi-final seven years ago.

'I've got a Mets game to watch'

Recently-crowned Olympic champion Zverev converted seven of 15 break points, and won 77 of 117 points in the match, to earn a 13th straight victory.

In the third round he will play wildcard Jack Sock, a former world number eight now ranked 184th, after the American knocked out Kazakh 31st seed Alexander Bublik with a 7-6 (7-3) 6-7 (2-7) 6-4 4-6 6-3 win.

Asked if he had been in a rush to finish the match, Zverev joked about having his eye on a Major League Baseball match later.

"I've got a Mets game to watch tonight," he said.

"I know that Albert is somebody that has a lot of wins over top-10 guys, that has beaten [Roger] Federer on a hard court so I know he's a difficult player," Zverev added.

"Once the match went my way the way it went, I did try to play as quick as possible. I did try to not give him time. I did try to keep on pushing."

Zverev was runner-up in last year's US Open, reaching his first Grand Slam final but losing to Austria's Dominic Thiem after squandering a two-set lead.

This year he is aiming to go one step better and land the maiden major title for which he has long been touted.

Winning gold at the Tokyo 2020 was backed up by another triumph at the Cincinnati Masters last week, ensuring he came into the final Grand Slam of the 2021 season in top form.

Trio create another Little Italy at Flushing Meadows

Elsewhere on Thursday, Italian sixth seed Matteo Berrettini overcame Frenchman Corentin Moutet in four sets.

The beaten 2021 Wimbledon finalist dominated a first-set tie-break but conceded the second set after being broken in the 10th game.

The 25-year-old world number eight took charge of the third and fourth sets with breaks of serve in the opening games, before clinching his first match point on Moutet's serve for a 7-6 (7-2) 4-6 6-4 6-3 win.

Berrettini, a US Open semi-finalist in 2019, will face Ilya Ivashka next after the Belarusian beat Canada's Vasek Pospisil 6-3 6-4 7-6 (7-5).

Fellow Italians Andreas Seppi and Jannik Sinner also advanced as three men from the Mediterranean country reached the US Open third round for the first time.

Seppi, 37, came from a set down to knock out Polish 10th seed Hubert Hurkacz, while 13th seed Sinner, 20, also needed four sets to beat American teenage wildcard Zachary Svajda.

Former top-20 player Seppi prevailed 2-6 6-4 6-4 7-6 (8-6) against the Wimbledon semi-finalist and meets Oscar Otte in the third round following the German's 6-4 6-4 6-2 defeat of American Denis Kudla.

Sinner won 6-3 7-6 (7-2) 6-7 (6-8) 6-4 and will take on France's Gael Monfils after the 17th seed beat American opponent Steve Johnson.

In other action, Canadian seventh seed Denis Shapovalov battled past Spain's Roberto Carballes Baena 7-6 (9-7) 6-3 6-0 to set up a third-round meeting with South Africa's Lloyd Harris.