The second-seeded Spaniard needed just an hour and 40 minutes to get the job done on Arthur Ashe Stadium against Robredo, who had upset Swiss master Roger Federer in the fourth round.
However, he was no match for Nadal, receiving an ironic cheer when he finally won a game at 0-2 in the second set.
Nadal will play Frenchman Richard Gasquet in the semi-finals on Saturday.
Robredo won the first point with an unreturnable serve but that was about as good as it got for the 31-year-old, who was constantly on the back foot as Nadal dictated play with heavy forehands and only 15 unforced errors for the match.
Nadal has yet to lose his serve in the tournament and did not face a break point against Robredo.
Robredo showed glimpses of form early in the third set but when Nadal broke in the fifth game the writing was on the wall.
Nadal broke serve for the seventh time before sealing the lopsided affair when Robredo sent a forehand long.
"I think I played my best match in the US Open this year," Nadal said. "Playing a little bit better every day is great. I am in the semi-finals and very happy to be here."
Earlier on Wednesday, Gasquet, who has a 0-10 record against Nadal, had recalled beating the Spaniard when they were 13-year-olds.
"I think I lost 6-4 in the third," confirmed Nadal.
"It was one of the first tournaments for me to play internationally, under 14. Richard was unbelievable. He's a nice guy and a good friend. We started together as kids and it's great to see him in the semi-finals in the US Open."
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