The hosts had not won the competition since 2007, while it was Panama's first appearance in the final and Jurgen Klinsmann's men had the cutting edge in the end.
Klinsmann was forced to watch the game from the stands after receiving a touchline ban following an incident in the semi-final, but he will have been pleased with the start his side made.
Holden's effort was the only real chance of the half as it turned out, with both sides struggling to create any opportunities of note, other than set-pieces and long-distance strikes.
The second half continued in the same vein until, after 68 minutes, Klinsmann's side took the lead through substitute Shea as he tapped home from close distance.
An Alejandro Bedoya cross came in from the right and, while it looked as though Landon Donovan would apply the finish, he completely miscued his effort, allowing Shea to steal in and prod home.
The US saw out the four minutes of added time and withstood heavy pressure from Julio Dely Valdes' side to secure the title, sparking jubilant scenes at Soldier Field.
