Team USA escaped with a 101-100 victory thanks to James, who sank the go-ahead layup with eight seconds left in regulation.
James finished with 23 points, six rebounds and six assists. Shayok recorded 25 points, three rebounds and two steals for South Sudan.
Team USA will conclude its USA Basketball Showcase with an exhibition game against Germany at 2 p.m. Monday in London.
Team USA rolled out its second unit of Derrick White, Anthony Edwards, Jayson Tatum, Anthony Davis and Bam Adebayo to start the second half.
That change ignited the United States, which outscored South Sudan 37-18 in the third quarter and closed things out on a 16-0 run to take the lead.
Team USA had no answer for containing South Sudan, which expanded its lead to 14 points entering halftime.
South Sudan went 22 for 35 from the floor (7 for 14 from deep) in the first half, and Shayok led the way with 14 points. Team USA went 15 for 36 from the floor (1 for 12 from deep), and James led the way with 12 points.
Team USA opened the game on a 12-2 run, and James led the charge by scoring six of those points.
But South Sudan weathered the storm thanks in part to Gabriel, who recorded six points and one rebound.
Team USA's starters will consist of Steph Curry, Devin Booker, Jrue Holiday, LeBron James and Joel Embiid.
South Sudan will start Carlik Jones, Marial Shayok, Bul Kuol, Nuni Omot and Wenyen Gabriel.
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