In a contest that finished at 00:51 local time in New York, Millman came from a set and a break down to inflict an extraordinary 3-6 7-5 7-6 (9-7) 7-6 (7-3) defeat on Federer.
"I just thought it was very hot tonight", Federer shared following the match.
"On court, he recognised that he may have got the great one on a rare night off, or an occasion where an ailment had blunted his brilliance", Fairfax media said in an analysis.
"There was no circulation at all".
In the women's draw, Naomi Osaka reached her first grand slam quarter-final with victory over fellow 20-year-old Aryna Sabalenka.
Asked to explain his performances over the last few months, Federer said: 'You know what, I explained Wimbledon already.
"It was very tough conditions, especially the first hour and a half". I've played in the daytime, you know, at 120 (degrees Fahrenheit, 49 Celsius).
"I think against Novak, he just has to bring it again, try to worry Novak, hope for another hot day, maybe".
There was no surrender - he wrestled with Millman through two tie-breaks - but in the endFederer simply ran out of energy and ideas.
He improved to 28-0 at the U.S. Open against opponents ranked outside the top 50, and here's another reason it wasn't all that surprising the way things went against Sousa: Djokovic is now 5-0 in their head-to-head series, taking all 14 sets they've played against each other.
"But John was able to deal with it better. He maybe comes from one of the most humid places on earth, Brisbane!"
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"But I got out of a tough second set, really found my feet and started to be a little bit more aggressive". Because I think if you do that, then you start behind the eight ball straight away.
"I had a shower, lay on the table and I didn't want to come back again", third-seeded Argentine Juan Martin del Potro said of how he spent the break in his 6-7 (5/7), 6-3, 7-6 (7/4), 6-2 victory over American John Isner.
"I am probably in a little bit of disbelief".
Kei Nishikori, runner-up in 2014, was also pleased to get through in three sets in blazing sunshine on Louis Armstrong Stadium. That's been a constant with me for, you know, ever since I played the game.
But his much-anticipated quarterfinal matchup against his old rival Novak Djokovic - what would have been their 47th meeting, and seventh at the US Open - was foreclosed by the Australian, who will now meet the Serb on Thursday.
He said: "I'll obviously remember this for a long, long time".
"When I have no time, I hit the best shots".
Carla Suarez Navarro ended Maria Sharapova's ideal record in night matches at the U.S. Open, reaching the quarterfinals with a 6-4, 6-3 victory.
Millman's tennis journey has rarely intersected with Australia's two highest profile players, who have enjoyed attention and wealth far beyond their achievements.
"John, well, I love his intensity", the Swiss champ said after his loss.