South Africa went into the game with four wins from four but their batters have struggled for fluency, with their top score in the group stage just 115.
The tricky pitch in New York, where they played three of their four group games, offers some mitigation and the more batter-friendly surface in Antigua allowed them to demonstrate the firepower in their top order.
Despite losing Reeza Hendricks early on De Kock and Markram took control, reaching 64-1 at the end of the powerplay that included a brutal 28 runs off a Jessy Singh over.
South Africa looked on course for a score in excess of 200 at that stage but USA continued to display the admirable spirit they have shown throughout this tournament.
Harmeet removed De Kock and David Miller in successive deliveries to check momentum, while left-armer Saurabh Netravalkar once again impressed with figures of 2-21.
USA chased down 195 in their opener against Canada and they began aggressively to try and keep up with the rate, but lost wickets at regular intervals, slipping from 53-1 to 76-5.
That brought Gous to the crease to join Harmeet with the game seemingly gone, but some extraordinary hitting brought them back into contention.
Gous, who is now the tournament’s top run-scorer with 182, reached his half-century from just 33 balls with two huge back-to-back sixes off Nortje.
He then hit two more in the 18th over from Tabraiz Shamsi that went for 22.
But Harmeet holed out to Tristan Stubbs at the start of the next over from Rabada, who showed all his class at the death to snuff out the USA’s challenge.
South Africa’s next match is against England in Saint Lucia on Friday at 15:30 BST, while USA take on fellow co-hosts West Indies at 01:30 on Saturday.