In the biggest upset of the tournament, Robredo demolished a badly out-of-sorts Federer 7-6(3) 6-3 6-4 in the fourth round, marking the first time in a decade the Swiss master has fallen before the quarter-finals at Flushing Meadows.
His straight-sets defeat left the New York crowd stunned by what they had witnessed in a match that was moved from Arthur Ashe Stadium to the smaller Louis Armstrong Stadium following a five-hour rain delay.
Robredo will now play either Nadal or Philipp Kohlschreiber in the quarter-finals, the long-awaited clash between Federer and Nadal in the Big Apple put on hold for at least another year.
"I feel like I beat myself, without taking any credit away from Tommy," Federer said. "I kind of self destructed, which is pretty disappointing.
"When things came to the crunch I just couldn't do it."
Federer's unforeseen loss to a player he had beaten in all of their 10 previous meetings overshadowed a remarkable turnaround by Daniela Hantuchova, who advanced to the quarter-finals for the first time in more than a decade.
The 30-year-old Hantuchova had not reached the last eight in New York since she was a teenager in 2002 but made up for lost time with a 6-3 5-7 6-2 victory over American wildcard Alison Riske.
"I guess the best things happen when you don't expect them," said Hantuchova, now ranked 48th in the world.
Hantuchova will have to wait another day to learn who her opponent will be after the fourth round match between Victoria Azarenka and Ana Ivanovic was postponed until Tuesday because of the foul weather.
However, it is already guaranteed that Italy will have a semi-finalist after Flavia Pennetta and Roberta Vinci won their fourth round matches to face each other in a quarter-final.
Vinci beat yet another Italian, Camila Giorgi, 6-4 6-2 in just over an hour, escaping before the U.S. National Tennis Center was drenched by a thunderstorm that sent players and spectators running for cover.
Tournament officials were again forced to cancel dozens of matches, before Pennetta returned to finish off in-form Romanian Simona Halep 6-2 7-6(3).
Pennetta has lost in the quarter-finals on three previous occasions and desperately wants to make it through to the semi-finals for the first time. She said achieving her goal would come at a heavy price because Vinci is one of her closest friends.
"I think it's going to be just a really tough match for both of us," Pennetta said.
"We know each other really well ... 20 years or more, because we live almost in the same place, just 35, 45 kilometres (away)."
A late bloomer, Vinci has hit her peak at an age when a lot of professional players begin to slow down.
The 30-year-old won just one singles match at the U.S. Open between 2001 and 2010 but in the past year and a half, she has made it to the fourth round or better in five of the last six majors, reaching a career high ranking of 11.
And she has also won three grand slam doubles titles, to share the world number one ranking with Sara Errani.
"I know that I'm not young, but I'm enjoying playing," Vinci said. "I have a high ranking so I'm happy, and I try to stay focused every single day."
New York's fickle weather has been a major talking point at the U.S. Open for years with each of the last five men's finals spilling into a third week because of rain delays.
For years, U.S. Tennis Association officials balked at the idea of building a roof because of the enormous cost of covering Arthur Ashe Stadium, the largest tennis stadium in the world.
But they have finally relented, announcing two weeks ago that they would commence a massive renovation program, which would include a roof, by 2016 at the earliest.