Millman – who saw off Roger Federer in the fourth round – was playing in his first quarter-final of a Grand Slam, but couldn’t rein in Djokovic.
Despite appearing to struggle at points during the match which contained some very long rallies, including a 27-stroke point, Djokovic emerged victorious after three hours on the Arthur Ashe Stadium court – 6-3, 6-4, 6-4.
Djokovic who has reached the semi-finals of the US Open every year since 2007, will now face Kei Nishikori who defeated him at the same stage four years ago.
But the former world No 1 congratulated his Australian opponent for his gutsy display.
“I was tested very well and I was on court for three hours,” Djokovic said.
“Credit to John for putting up a great battle.
“He’s truly a great fighter.
“He’s had an amazing tournament and to come out after his Federer match, he deserves a round of applause.”
Millman changed his shirt during the second set as both players seemed to struggle with the humidity.
Although there was an element of controversy, the US Open officials have cleared Millman of any wrongdoing.
A statement read: “At two games all in the second set of the Novak Djokovic-John Millman match, Millman approached the chair umpire to note his excessive sweating and the moisture it was leaving on the court.
“The chair determined that the surface was dangerous enough to invoke the ‘Equipment Out of Adjustment’ provision in the ITF Duties and Procedures for Officials and allowed Millman to go off court to change clothes/shoes. Both players agreed that he should do so.
“Because the chair umpire deemed the situation within the ‘Equipment Out of Adjustment’ provision, Millman was not charged with an official change of attire or bathroom break.
“A similar situation occurred between the fourth and fifth sets of last night’s Rafael Nadal-Dominic Thiem match, when Thiem was allowed to retrieve dry shoes from the locker room, which extended the normal amount of time that elapses between sets.”