Novak Djokovic's bid for a 21st major title that would complete a calendar-year Grand Slam picked up pace on Thursday as the world number one cruised into the US Open third round with a 6-2 6-3 6-2 thrashing of Tallon Griekspoor.

Having shaken off the rust in a spotty four-set opening match against 18-year-old Holger Rune on Tuesday, Djokovic was sharper and much more focused against the 25-year-old Dutchman.

Just like his first round contest Djokovic dominated early on but this time the 34-year-old Serb never let his foot off the gas as he registered his 77th win at the US Open.

Only three men have won more matches at the US Open -- Jimmy Connors (98), Roger Federer (89) and Andre Agassi (79).

Djokovic, playing his first event since the Tokyo Olympics, found the intensity that had been lacking against Rune, speeding through the opening set in 30 minutes.

"I came out on court with the right intensity, the right focus," said Djokovic. "Better definitely than the first-round match.

"It was important I came up with the goods.

"I'm very pleased with the level of my tennis. All is going in the right direction."

The highlight of the evening for Griekspoor came in the second set when he broke Djokovic but the world number one would break right back and then hold serve to take the set and a 2-0 lead.

Griekspoor had rallied from 2-1 down in his opening match to collect his first ever Grand Slam win but there was no coming back against the top seed.

Djokovic then broke Griekspoor twice in the third set before sealing the contest with his 13th ace.

Afterwards Djokovic basked in the applause of the crowd, something he had not done for his opening round victory after the Arthur Ashe Stadium crowd had roared on his Danish opponent throughout the match. After beating two young opponents playing in their first US Open main draw, Djokovic next faces Japan's Kei Nishikori, the 2014 US Open runner-up.

"I have very good score against him," said Djokovic, who swept aside Nishikori 6-2 6-0 in the quarter-finals of the Tokyo Olympics. "He's one of the quickest and most-talented players that I've seen in my career.

"He likes to hit the ball early, protect the line, but I know his game well."