Djokovic, a two-times champion at Flushing Meadows, struggled with the humidity at Arthur Ashe Stadium but kept his cool mentally, saving the only break point he faced in the first set and wrapping up the opener in an hour.
"(I was) very tested," Djokovic said. "Almost three hours. It's midnight now. Credit to John for putting up a great battle."
Millman is used to the searing heat in his native Brisbane, but needed to leave court to change with the score level at 2-2 in the second, telling the umpire he was unable to put the ball in his pocket because his shorts were soaked through with sweat.
The U.S. Tennis Association said in a statement that Millman was sweating so profusely that the moisture dripping onto court had made the surface too dangerous to play on.
"These night matches the humidity goes through the roof," Millman said. "It is tricky, but it's the same for both people. You're dripping.
"But that's no excuse or anything. I'd play in a swimming pool if I got to play a quarter-final every week at a Grand Slam. That would be pretty fun."
Millman, who beat Roger Federer in the previous round, returned after a brief interval but found no joy against Djokovic's serve and the Serb broke the Australian in the penultimate game before serving out the second set.
The match was marked by long rallies, with 57 of the pair's exchanges stretching to more than nine shots.
"I was struggling, he was struggling," Djokovic added. "Changing a lot of t-shirts, shorts and just trying to hang in there and find a way to win the match.
"Not easy conditions to play in, but it's the same for both players."
Djokovic broke early to take a 3-1 leave in the third set but a lapse in concentration allowed Millman to draw level.
The Serb was given a time violation warning and double faulted to offer Millman a break point opportunity before losing his first serve after running down the shot clock a second time.
A forehand error from Djokovic let Millman level at 3-3 but the sixth seed carved out three break points in the next game, converting the third before serving out the match and sealing the win with a backhand volley in two hours, 48 minutes.
(Reporting by Simon Jennings; Editing by Greg Stutchbury)
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