Agudelo scored from close range after being fed through by another of the American debutants, Norwegian-born Mikkel Diskerud.
It was the first loss for new coach Pitso Mosimane and came against the run of play.
But despite a heroic performance from Steven Pienaar, captaining the side for the first time, and a debut for the Leeds United striker Davide Somma, Bafana gave a full house at the Green point Stadium little to enthuse over.
Somma might have been given a penalty after 10 minutes after being tugged down in the American area but the Kenyan referee Silvester Kirwa waved play on.
But the debutant was involved in a sharp one-two just four minutes later with fullback Anele Ngcongca, who came storming down the right flank but had his effort on goal smothered by American ‘keeper Brad Guzan.
The Aston Villa goalie made a similar stop off his line to deny Bernard Parker in the 20th minute as Bafana Bafana picked up the tempo, winning much of the loose midfield ball.
But with two fullbacks pushing high, the slow circulation of the ball by South Africa saw them lose the impetus.
The Americans had their first effort after 22 minutes when Robbie Rogers shot unmarked from the edge of the area but Itumeleng Khune saved.
Khune had two more saves to make before the break and 10 minutes into the second half dealt easily with substitute Teal Bunbury’s effort.
Somma had another half-heated claim for a penalty before he was taken off on the hour mark, replaced by Sthembiso Ngcobo.
Ngcobo tried from a tight angle in the 65th minute but hit a ferocious shot into the side netting.
A bevy of second half changes meant the game lost some of its sting and as Pienaar tired so even more of the fluidity was lost.
Pienaar did have a mazy run after picking up on a loose ball in the 72nd minute but his shot was half-blocked for a corner. He went off for the final 11 minutes replaced by Daylon Claasen, on for his first cap.
Siyabonga Sangweni had a half chance with eight minutes to go from a corner.
Bafana: Khune; Ngcongca (Gaxa 79’), Sangweni, Gould, Masilela, Dikgacoi (Jali 60’), Khuboni (Pattison 88’), Tshabalala, Pienaar (Classen 79’), Parker (Erasmus 88’), Somma (Ngcobo 60’)
USA: Guzan; Ream (Borchers 67’), Bornstein (Spector 46’), Lichaj, Goodson (Agbossoumonde 87’), Bedoya (Diskerud 78’), Carrol, Gaven, Pause, Rogers (Agudelo 61’), Findley (Bunbury 46’)