Djokovic downed Millman 6-3 6-4 6-4 in a dramatic war of attrition to end the unseeded Australian’s gallant run, reaching his 11th semifinal in New York in the process.
The reigning Wimbledon champion and 13-times major winner’s victory vaulted him into a last-four meeting on Friday with rejuvenated 2014 runner-up Kei Nishikori.
The sixth seed was full of praise for the Australian, who had stunned world No.2 Roger Federer in the previous round.
“(I was) very tested. Almost three hours. It’s midnight now. Credit to John for putting up a great battle,” Djokovic said on court.
“He’s a truly great fighter … he’s had an amazing tournament, first quarterfinals, he won against Roger a couple of nights ago. To come out after that kind of win and fight here for three hours, he deserves a round of applause, definitely.
“(At net we shared) respect for each other. I’ve played him only once in my career, a month ago in London on grass (at Queen’s Club).
“I’ve known him, he’s been around for quite a few years and he’s been known around the tour as a guy with a hard-working ethic and you can see that – he fights for every point and he’s never going to hand you the win.
“He played an amazing tournament.”