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.
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 yesterday.
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.
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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.
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.