Agudelo, who turns 18 next week, scored from close range after being fed through by another new cap, Norwegian-born Mikkel Diskerud to hand South Africa their first defeat in four matches since hosting the World Cup in June and July.
"I'm speechless, I don't know what to say," said the Colombian-born Agudelo.
"As I saw the ball go in, I didn't believe it, I thought it was going to get called back for offside or something.
"I really, truly didn't believe it. So many people are here watching me and I score the goal. It's an amazing feeling," added the forward, fast tracked from the U.S. under-17 side to the senior squad for the friendly in front of a sell-out crowd of 52,000 at the Green Point Stadium.
Agudelo, one of five new caps in the U.S. side, only made his senior debut for New York Red Bull towards the end of the American season.
U.S. coach Bob Bradley said the teenager had made an impact then and "so we thought this was an opportunity to bring him into his first national team camp".
"We had a plan to use him as a sub in the second half. We think there is something there and we are excited to work with him."
FRINGE PLAYERS
With both sides electing to play a host of fringe players, the match provided few real chances although it was dominated by the midfield toil of Steven Pienaar, captaining South Africa for the first time.
The hosts handed a debut to striker Davide Somma, born in Johannesburg but raised in the U.S., and he was involved in a sharp one-two inside the first quarter-hour with full-back Anele Ngcongca, who came storming down the right flank but had his effort on goal smothered by American goalkeeper Brad Guzan.
U.S. captain Guzan made a similar stop off his line to deny Bernard Parker in the 20th minute as Bafana Bafana picked up the tempo.
The U.S. had their first effort after 22 minutes when Robbie Rogers shot unmarked from the edge of the area but it was saved.
A bevy of second-half changes meant the game lost some of its sting and as Pienaar tired so even more of the tempo was lost.
The Everton midfielder did have a mazy run after picking up on a loose ball in the 72nd minute but his shot was half-blocked in South Africa's best chance of the second half.
