In Wednesday's other quarter-final, Marin Cilic was ousted in five sets by Kei Nishikori, despite winning more points in the match and creating four more break point chances - such are the fine margins often required to win tennis matches.
Serbia's Djokovic beat the Japanese 21st seed 6-3 6-4 6-2 to set up a meeting with Juan Martin del Potro.
Juan Martin del Potro is advancing to the US Open final for the first time since winning the tournament in 2009.
Of the now nine grand slams he has played since returning, Del Potro has reached the quarter-finals twice, the semi-finals twice and, at last, another final, where he awaits the victor of Novak Djokovic's clash with Kei Nishikori.
If he beats Del Potro to equal Sampras, only Roger Federer (20) and Nadal (17) stand above him in the all-time list. I think was 2-All in the first, 15-Love, something like this in the first set, that I felt it.
"I don't like to see him suffering like today".
While leading 4-3 in the first set Nadal got his right knee taped, before later ripping it off and having it re-taped early in the second during a medical timeout in which he also had his leg massaged. But he was walking with a hitch in his step and had the trainer out to retape the knee early in the second set.
As del Potro continued slamming serves at faster than 130 miles per hour (210 kph), whipping that trademark forehand, and even making hay with his much-improved two-handed backhand, Nadal offered less and less resistance. "It was so hard for me to keep playing at the same time that way, having too much pain". In the last three years, the Serb is 10-0 against Nishikori, dropping just three sets out of 25 in the process - it will take a considerable swing in head to head momentum for this match to produce a shock.
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That included nearly five hours to defeat Dominic Thiem in an epic quarter-final which stretched into the early hours of Wednesday morning. But, you know, he's got two days now to recover, so he's going to be fresh.
A dejected Nadal said later: 'I had some issues during the tournament.
"The problem is this time it was something a little bit more aggressive because it was in one movement". Devastating for it to happen in a Grand Slam SF. In a post-match news conference Friday, he was as frustrated as he was glum to have lost the chance to play for his 18th career major title.
"Is not an injury that tells you six months off, you are back".
"That's frustrating. Is tough for me". It's not about losing. After that, I was just trying to see if in some moment the thing can improve during the match. "I am playing well. Especially after coming from injury, I'm enjoying this challenge".
Del Potro led a standing ovation on Arthur Ashe Stadium when Nadal walked gingerly off court. Lot of people in this room, including myself, never thought that at the age of 32 I will be here fighting for titles, fighting for the first position of the rankings.
"All my career everybody say that because of my style, I will have a short career". I still here. I still here because I love what I am doing'.