The 31-year-old South African and No. 28 seed defeated No. 12 Pablo Carreno Busta of Spain, 4-6, 7-5, 6-3, 6-4 in 2 hours, 55 minutes in the first U.S. Open semifinal Friday evening in Arthur Ashe Stadium.
After closing out the match on his serve, Anderson climbed over a flower pot and into the stands to hug his wife, Kelsey, and others in his player's box.
"I really had to dig deep there," Anderson, who smacked 22 aces in the match, said in his on-court interview with ESPN. "I think just my emotions at the end summed it up. I was just over the moon at the end. I'm going to allow myself tonight to really celebrate tonight's win."
Anderson improved to 3-0 against Carreno Busta, but he hasn't had any success against either Nadal or del Potro. Nadal leads Anderson 4-0 and Del Potro leads Anderson 6-0.
"The way Anderson is playing, he's going to be a problem for either guy in the final," ESPN's Darren Cahill said on air.
Anderson, who played college tennis at the University of Illinois and resides in Gulf Stream, Fla., is the first South African man to reach a Grand Slam final since Kevin Curren advanced to the Wimbledon final in 1985. Johan Kriek, who was born in South Africa before becoming a naturalized American citizen, won the Australian Open in 1982.
The bottom half of the draw opened wide after No. 2 Andy Murray withdrew before the tournament with a hip injury and No. 4 Alexander Zverev and No. 5 Marin Cilic lost during the first week of the tournament. Carreno Busta became the highest remaining seed in the bottom half after No. 10 John Isner lost in the third round.
But it is Anderson and his huge serve -- he has reached 137 mph during the tournament -- that has come through to the final on the bottom half. The result is by far the best of his career, although he did reach the fourth round at both the French Open and Wimbledon this year.
He missed the Australian Open in January with a hip injury and said he was concerned he might have to have surgery and miss the remainder of the year.
"It was very difficult at the end of last year," he said. "I was told that I probably needed to have surgery on my hip.
"Here I am just nine months after thinking I might have to undergo a year's worth of recovery for surgery."
Carreno Busta faced an unprecedented draw early, facing four qualifiers through the first four rounds. He didn't drop a set through his first five matches.
The Spaniard earned the only break in the first set in the seventh game and took the first set in 34 minutes, 6-4. He played his typical steady, if unspectacular, brand of tennis, earning two winners against just one unforced error.
In the second set, Anderson broke Carreno Busta twice. He took the set when the Spaniard double-faulted at 5-6, 30-all and Anderson then smacked a forehand winner into the corner on set point.
Anderson took the third set on his third set point, serving a 132-mph ace to take a two-sets-to-one lead.
Anderson earned a critical break in the fifth game of the fourth set, taking control of the match for good when the Spaniard shanked a forehand wide on break point. Anderson served out the match on his serve when Carreno Busta netted a forehand.
"This means the absolute world to me," Anderson said.