"I really don't know what to say right now", Anderson said in his ESPN on-court interview.
28th seed Anderson beat the Spanish 12th seed 4-6, 7-5, 6-3, 6-4.
Speaking to reporters afterwards, Anderson - who never progressed beyond the fourth round of a major before this year's US Open - said: "It's definitely an unbelievable feeling being in this position and have worked very hard to get here".
No. 1 Nadal will be a significant favorite Sunday against No. 32 Kevin Anderson of South Africa, who beat Pablo Carreno Busta, 4-6, 7-5, 6-3, 6-4, to become the lowest-ranked US Open finalist since the ATP's computer rankings began in 1973. But I did get to hang out with my family and see my little cousin's soccer games and go to weddings and baby showers and stuff.
In the second set, Anderson broke Carreno Busta twice.
"He has had an fantastic year and been very consistent - quarterfinals at the French Open and semis here in NY - so he's obviously very confident". I think I play very good again. He becomes the first man from the rainbow nation into a grand slam semi-final since Wayne Ferreira in 2003.
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Raheem Sterling will miss the game due to a a one-match suspension following his red card at Bournemouth. You have got to be masters of both of those if you are going to win the Premier League.
In the first of three posts, Williams wrote: "There are NO words to describe how proud and how happy I am for @Madison_Keys. and @SloaneStephens for making the United States open finals". The South African won his opening three rounds in straight sets against JC Aragone, Ernests Gulbis and Borna Coric respectively. It is a first-ever Grand Slam semifinal for both men in the second match on Arthur Ashe.
Anderson, 31, will contest his maiden major final against top seed and 15-time slam champion Rafael Nadal following Friday's 4-6 7-5 6-3 6-4 win over 12th seed Carreno Busta at Flushing Meadows. "When I wasn't playing, like, of course I loved my time off, but when I got back to playing tennis, it was, like, this is where I want to be".
"Rafa just play even better the last three sets of the match, and I couldn't hit my backhand as good as I did in the beginning of the match", said Del Potro. "Still obviously a very hard match ahead of me, but I think right now I'm just trying to unwind a little bit and just enjoy sort of today's match".
However, his last loss at this stage came on the same NY hard courts in 2009 at the hands of Del Potro, who went on to shock five-time champion Federer in the final.
"I have played both guys a few times", said Anderson. "I feel like I've kept my head down and kept working hard".
Nine months removed from a hip injury that caused him to drop out of the Top 75 in the world, Anderson has achieved the unimaginable.