Anderson, 31 years old and ranked 32nd in the world, is the lowest-ranked Grand Slam finalist since 38th-ranked Jo-Wilfried Tsonga fell at the 2008 Australian Open final.
"I don't know if the team hug was appropriate after the semi-finals, but it felt like the right thing to do", he said.
Still, the lanky South African thinks the journey has been worth it.
Golfing compatriots and major winners Charl Schwartzel and Louis Oosthuizen watched him win Friday on the NY hardcourts to reach the brink of a breakthrough win at 31.
Nadal ended the 2009 champion's ordeal with a splendid backhand passing shot on his first match point, four years after his last title at Flushing Meadows. Nadal hopes to win his 16th career grand slam and his third in the US Open. Anderson broke on the next point.
"I always try to practise with him because it's really important to me, to be near the best players and practise with them", he said.
Two games later Anderson saved a pair of set points, but a third was quickly snatched up by Carreno Busta as a serve out wide was returned into the net.
The 6ft 8in (2.03m) Anderson 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 the almost three-hour contest.
The Spaniard is looking to win his first grand slam title away from the French Open since the second of his titles in NY in 2013 and match Federer by claiming two slams this season.
Carreño Busta is the 10th man over the past 25 years to reach the US Open semifinals without having dropped a set.
The South African had the ideal start to the third set especially when he strolled to a comfortable service hold before earning a 0-40 lead on the return.
The likes of fourth seed Alexander Zverev, seventh seed Grigor Dimitrov and eighth seed Jo-Wilfried Tsonga then went out in the early rounds. Kelsey played golf in college, while Kevin played tennis for the Illini.
The key to this match, however, will be the battle between Anderson's serve and Carreno Busta's return. He played his typical steady, if unspectacular, brand of tennis, earning two winners against just one unforced error.
He was knocked out at Wimbledon in 2014, 2015 and this year in the fourth round.
Neither Carreno Busta nor Anderson has played in a semifinal at any Grand Slam tournament.
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