Number three Nadal booked a spot in the semi-finals by rallying past Federer, with the Swiss player saving four match points in a 5-7, 6-4, 6-3 loss.
The pair have met a total of 31 times, with Nadal winning 21 of those.
"My movement got better, with more intensity," said Nadal, undefeated on hardcourts in 2013. "I put in more balls on the return, and controlled the baseline, something that didn't happen the first set and a half. The match was very close. I played some good points in important moments."
"Credit to him for hanging in and getting back some tough shots," said five-time champion Federer, who will fall to seventh in the world as a result of his defeat.
"I have some disappointment, I could have played better late in the second and early in the third.
"But my tactics were working most of the time. I served well for most of the match, but when I didn't he was able to step it up."
World number one Djokovic fell 7-6 (7/5), 3-6, 7-5 to unseeded John Isner as the Serb's attempt to set another tennis record ended in defeat.
Two-time champion Murray was eliminated 6-3, 6-4 by Tomas Berdych, leaving the Scot to head for New York and his US Open title defense, beginning August 26, with plenty to work on.
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