Belize, whose mostly amateur and semi-professional squad are playing in their first Gold Cup, fell behind after just 12 minutes when Wondolowski fired home from close range.
Wondolowski then added a second in the 37th minute with a diving header from an excellent Kyle Beckerman cross.
Belize gained some reward for their efforts when they pulled a goal back after Ian Gaynair was left unattended to head in a cross from Elroy Smith in the 40th minute.
The joy was short-lived, however, and the hosts restored their two-goal advantage within a minute via another diving header from Wondolowski.
After the break, goals from substitute Stuart Holden, defender Michael Orozco and a Landon Donovan penalty completed the rout for Jurgen Klinsmann's side, who are looking for their fifth Gold Cup title.
After an uneventful first half, Barrantes made the breakthrough with a well-struck left-foot shot from the edge of the area in the 51st minute.
Barrantes thought he had a second with another strike from distance in the 67th minute but Jairo Arrieta was deemed to be in an offside position.
Arrieta made amends four minutes later though, poking home at the second attempt, after good work from substitute Kenny Cunningham.
The contest was over when Barrantes virtually passed the ball into the net, from 20 yards out, beating the slow-reacting keeper Odelin Molina with a few minutes remaining.