The 12-time Grand Slam title winner will face Richard Gasquet for a place in Monday's final after the French eighth seed clinched a rollercoaster 6-3 6-1 4-6 2-6 6-3 win over David Ferrer, the Spanish fourth seed. (Agencies)
World number two Nadal, the 2010 champion, took his hardcourt streak this year to 20-0 and his match record to an astonishing 58-3 with nine titles since his return in February after a seven-month injury layoff.
In a ruthless one hour, 40 minute demolition of Robredo, who had knocked out five-time champion Federer in the fourth round, the 27-year-old French Open champion took his perfect run of unbroken service games to 67 at the tournament.
He romped through the first set in just 22 minutes, allowing Robredo only five points, and was 2-0 up in the second before the 31-year-old got on the board.
Another break in the seventh game helped Nadal on his way to a two-set lead and breaks in the fifth and seventh games of the third helped put Robredo out of his misery.
It was the shortest US Open quarter-final since 1988, when Ivan Lendl beat Derrick Rostagno.
Nadal finished with 28 winners to Robredo's 10 and didn't give up a single break point as the world number two claimed an eighth win in eight meetings against his countryman, who has only won one set during that one-sided series.
"I am very happy to be in the semi-finals. I think I played my best tennis of this US Open. It's good to feel better with every match," said Nadal.
Gasquet, 27, whose only previous appearance in the last four at a major was at Wimbledon in 2007, is the first Frenchman to get to the semi-finals in New York since Cedric Pioline in 1999.
The victory was only his second in 10 meetings with Ferrer, a series which had also seen him claim just two sets out of 20.
Next up is Nadal, against whom he has lost all 10 meetings as a professional, although he did beat the great Spaniard in their junior days.
The 12-time Grand Slam title winner will face Richard Gasquet for a place in Monday's final after the French eighth seed clinched a rollercoaster 6-3 6-1 4-6 2-6 6-3 win over David Ferrer, the Spanish fourth seed.