A grand slam semi-final represented a new experience for both men but it was 12th seed Carreno Busta who appeared to adapt quickest in the early stages as he took the first set.
The 31-year-old Nadal, with his teeth firmly in his prey, showcased his defensive class to turn things around on match point and set up a strong chance for more grand slam silverware.
Aiming to become the first South African man to reach the US Open final since Cliff Drysdale achieved the feat in 1965, during the amateur era, Anderson credited his progress to minor improvements in his game.
The 31-year-old will face either world number one and two-time champion Rafael Nadal or 2009 victor Juan Martin del Potro in Sunday's title match. It all started in the fourth game when Anderson produced some of his best returns to earn his first break points and the aggressive play from him was simply too good for the stubborn defense of Carreno Busta, taking the lead for the first time in the match. Anderson has won just one set against Nadal in all four meetings, and this is their fourth match on hard court.
There was a tense final game to negotiate but a Carreno Busta forehand hit the net, sending Anderson up into the stands on a victory lap.
After six consecutive service holds to start the match with, a break point finally surfaced as a couple of unforced errors caused Anderson to play a loose game, eventually gifting the break to the Spaniard after sending a backhand long. Instead, the South African hung tough and emerged a 7-6 6-7 6-3 7-6 victor to make his maiden Slam semifinal. "I think it should been an exciting semis", Federer said.
"I thought the beginning of the match, I felt a little bit nervous", Anderson said.
South African tennis player Kevin Anderson.
Anderson, who stands at 2.04 metres tall, climbed into his player's box to embrace his wife, brother and coach Neville Godwin after Carreno Busta's forehand found the net to finish their almost three-hour contest.
"Everybody knows Rafa, he's an incredible tennis player and one of the best ever", said Carreno Busta. "I was not playing bad in the first set but I lost it so some things had to change". He thanked his family for their support after his win on Friday, with brother Greg getting a special mention for nurturing his Grand Slam dream from a young age.
"It will be an interesting match, and I'm very excited to go out there and compete in the semifinals". Del Potro was the U.S. Open champion in 2009, when he beat Nadal in the semifinals and Roger Federer in the final.
"Ultimately, such a sacrifice would compromise my results and any hope of competitive representation for South Africa at Grand Slam tournaments". Carreno Busta has been serving very well so far this tournament.