Djokovic is bidding to become just the third man to complete a calendar Grand Slam and the first to sweep all four Majors in a year since Rod Laver in 1969.

The No.1 seed, who is also pursuing a record-breaking 21st slam crown – currently level with injured stars Rafael Nadal and Roger Federer on 20 – outclassed Griekspoor in one hour, 39 minutes on Friday (AEST).

Awaiting Djokovic is 2014 US Open finalist and Japanese star Kei Nishikori in the third round.

Djokovic, who withstood a spirited challenge from Holger Rune in the opening round before the teenager succumbed to cramps, asserted his dominance against Griekspoor from the outset on Arthur Ashe Stadium.

Boasting a 14-0 record in second-round matches at the US Open, Djokovic only lost one point on his first serve in the opening set and fired down five aces, while hitting 13 winners and converting two of his three break points.

While world No.121 Griekspoor managed to break Djokovic's serve in the second set, the Serb was typically efficient as he builds towards another shot at history in New York.

Coming to the net more in the third set, Djokovic was determined to get off the court as quickly as possible and he did just that – saving three break points en route to another third-round appearance at the year's final slam.