Millman battled to a 3-6, 7-5, 7-6, 7-6 triumph on Arthur Ashe Stadium at Flushing Meadows to reach the last eight at a Grand Slam for the first time.

The 29-year-old will take on Serbian two-time US Open winner Novak Djokovic, who swept aside Portugal's Joao Sousa 6-3, 6-4, 6-3.

Millman, who became the first player ranked outside of the world's top 50 to beat Federer at the US Open, said he was "in a little bit of disbelief" at what he had achieved.

Federer admitted the sweltering conditions had played their part in his downfall.

The Swiss star showed signs that the heat was affecting his game during the match as he became unusually vocal and also complained about the noise of the crowd.

"It was very hot and one of those nights where I felt I couldn't get air," Federer said.

"I just struggled in the conditions and it was one of the first times it has happened to me.

"You just keep sweating and lose energy. 

"At some point I was just happy the match was over."

Japan's Kei Nishikori and Croatian Marin Čilić will meet in a repeat of the 2014 final after both players came through their respective fourth-round contests.

Čilić, who beat the Japanese to claim his first and only Grand Slam title four years ago, proved too strong for Frenchman David Goffin with a 7-6, 6-2, 6-4 victory.

Nishikori overcame German Philipp Kohlschreiber 6-3, 6-2, 7-5.

In the women's draw, Russian Maria Sharapova, who won the event in 2006, was beaten 6-4, 6-3 by Spanish 30th seed Carla Suarez Navarro.