The 19th-seeded Robredo, who came into the fourth-round match with an 0-10 record against the 17-time major champion, dismissed him 7-6 (7-3), 6-3, 6-4 on the Louis Armstrong court in New York after play was suspended for 4 1/2 hours by heavy rains.
The Swiss icon's exit foiled fans' hopes of seeing him matched against fellow superstar Nadal in the quarterfinals -- the two have never faced each other in the U.S. Open.
The Spanish star made it there without Federer, rallying after a dropped first set to dispatch 22nd-seeded German Philipp Kohlschreiber 6-7 (4-7), 6-4, 6-3, 6-1.
Nadal, who claimed his only U.S. Open title in 2010, improved to 19-0 on hard courts this year and comes into his match against Robredo with a 6-0 all-time record against his countryman.
Ferrer now goes on to face eighth-seeded Richard Gasquet of France, who got past No. 10 Canadian Milos Raonic, 6-7 (4-7), 7-6 (7-4), 2-6, 7-6 (11-9) in a 4-hour, 40-minute struggle.
Celebrity Families of 2014 [PHOTOS]