Anderson, coming into the final grand slam of the year holding the 28th seed has been phenomenal in his performances.
The 31-year-old right handed South African player fought back from a set down to sweep out Busta in four sets 4-6 7-5 6-3 6-4.
Kevin Anderson of South Africa is aiming to become only the second South African in the Open Era to make the final of a Grand Slam.
At 32 in the world, he is the lowest-ranked men's singles finalist at the US Open since the rankings began in 1973.
Carreno Busta's serve was the first to come under any kind of pressure in the sixth game of the match, but he held from 30-30 before striking what proved the decisive blow in the opener as Anderson fired a backhand long to hand him the break. A bullet-like backhand victor sealed the second set for the South African, leveling the match at one set all.
Anderson was soon 5-4 ahead, hitting his 100th ace of the tournament in the process before leveling the tie in the 12th game courtesy of a Carreno Busta double fault and a fierce backhand victor.
Anderson amplified up his aggressiveness on the court, charging the net at any opportunity, broke serve in the fourth game for a 3-1 lead. Their only other clash was in 2013 on Casablanca clay, which Anderson won 6-3, 6-3. "I think it should been an exciting semis", Federer said.
"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.
I am proud of Kevin for sticking it out and surviving in one of the toughest global sports. "I'm going to allow myself tonight to really celebrate tonight's win".
Through dogged determination, he slowly climbed the ladder, reaching a career top-10 in October 2015 after reaching his first Grand Slam quarter-final at the 2015 US Open.
"It will be an interesting match, and I'm very excited to go out there and compete in the semifinals". Interestingly, it is the first time in Grand Slam history that someone has faced four qualifiers in a row. The Spaniard did, after all, get very shaky in losing early in the tournament here in the last two years against opposition he was expected to beat, and he has so far had a comfortable draw.
'If he's in the final, he can beat everyone.
South African tennis player Kevin Anderson.
Starting the fourth set serving, it was a bright start for Carreno Busta as he looked to have regained his composure and found the momentum.