Nadal was every bit as dominant in a 6-0 6-2 6-2 victory.
This was supposed to be the long-awaited first meeting in New York between Nadal and Roger Federer but Robredo spoiled the party in the fourth round.
It cannot have felt like much of a prize as he won only five points in a first set that lasted just 22 minutes.
Robredo had managed only one set in six previous meetings with Nadal, who has an excellent record against his fellow Spanish baseliners.
There was a huge cheer from the night crowd on Arthur Ashe when Robredo finally won a game in the second set, but by that stage he was already 2-0 down.
Nadal has not had his serve broken all tournament and Robredo could not put him under any real pressure.
As soon as Nadal broke in the fifth game of the third set the match was as good as over, although to his credit Robredo did not stop fighting.
The victory took Nadal’s record on hard courts this year to 20 wins and no defeats, and he will be a big favourite to defeat Richard Gasquet in the semi-finals.
Nadal said of his performance: “I’m happy. I think I played my best match of the US Open. I’m playing a little bit better every day and it’s a great year. I’m very happy to be in the semi-finals. I want to enjoy every moment.”
Earlier, Gasquet posted a landmark five-set victory over David Ferrer.
The Frenchman is one of the most talented players on tour but too often his nerve has failed him in big matches.
Having dominated the first two sets, Gasquet looked set to suffer another heartbreaking loss when fourth seed Ferrer fought back to level the match.
But this time it was Gasquet who came good in the decider to clinch a 6-3 6-1 4-6 2-6 6-3 victory after three hours and 23 minutes.
Of the 27-year-old’s last six five-set defeats at grand slams, five of them have come after he was two sets up.
But there have been signs this season that Gasquet was ready to leave his reputation behind him.
And he showed in his fourth-round victory over Milos Raonic, where he saved a match point in the fourth set before going on to win in five, that he could battle and win.
Somewhat ironically, the only other time Gasquet has reached a grand slam semi-final was at Wimbledon six years ago when he came back from two sets down to beat Andy Roddick before losing to Roger Federer.
Gasquet said: “I’ve lost some (five-setters), but I won some, too. So it’s in the middle.
“It’s always difficult when you are losing this kind of match, especially when you have been winning. At 5-2 in the fifth, I really wanted to close that match to win, because it’s Ferrer, centre court in the US Open, so it’s a big chance for me to go to the semis.
“I knew in the fifth set it was a very important set for me. For sure, it’s one of my biggest victories.”
The Frenchman’s one-handed backhand is the most elegant shot in tennis and it was firing on all cylinders in the first two sets.
Ferrer is a ferocious competitor, though, and an early break in the third set changed the momentum of the match.
But it was the Spaniard that cracked in the end, the man known as the little beast serving a double fault on break point in the sixth game of the fifth set.
Worringly for Gasquet, he has lost all 10 of his professional matches against his former junior rival Nadal, who is just two weeks older