The measure to allow breaks in matches was implemented for three days in the opening week as the players battled sopping humidity and scorching heat.
Federer was scheduled to play 55th-ranked John Millman of Australia in the fourth round later on Tuesday.
It was the 37-year-old's earliest loss at a slam since the Australian Open in 2015 and the first time he has ever lost to a player ranked outside the top 50 in NY.
Djokovic argued with the umpire in the third set too.
Conversely, it had been five years since Roger Federer exited a US Open before the quarter final stages, last failing in the round of 16 at the 2013 tournament where he was bested by Spaniard Tommy Robrero. Definitely a player I've looked up to throughout my career.
'But I got out of a tough second set and really found my feed, made a decision to be a little bit more aggressive.
Djokovic, however, was able to keep his cool just long enough to finish off Sousa with another late break.
But that only delayed the inevitable as Nishikori kept his focus to seal the win and extend his flawless record against the German to 3-0. He was manipulating me around the court, " Millman said.
'I'm probably in a little bit of disbelief, ' he said in his on-court interview.
Nishikori will next face either seventh seed Marin Cilic, which will be a rematch of the 2014 final, or Belgian 10th seed David Goffin. Keys advanced by beating No. 29 Dominika Cibulkova 6-1, 6-3.
After serving successive double faults in the fifth game, Federer missed two routine volleys before wrapping up the first set at the third attempt and he was then forced to save seven break points in a mammoth service game lasting 14 minutes early in the second.
Not since Pat Rafter handed a tantrum-throwing Federer a tennis lesson on the then-18-year-old's grand slam debut at Roland Garros in 1999 had an Australian conquered the great Swiss at a major.
Naomi Osaka reached her first grand slam quarter-final with victory over fellow 20-year-old Aryna Sabalenka.
Millman, unseeded and ranked 55th in the world, sealed the win in three hours and 34 minutes.
Millman fought back from being down a break early in the fourth set to force a tiebreak. Suarez Navarro let the 22nd-seeded Sharapova create her own problems.
The 32 degree celsius heat, though, is much tougher on Djokovic, who showed the same blank expression, rosy cheeks and sweat-soaked shirt as during his first-round match last week.
"Credit to Jaoo for fighting well with a lot of intensity on the court".