Belize, whose mostly amateur and semi-professional squad are playing in their first Gold Cup tournament, fell behind after 12 minutes when Wondolowski fired home from close range after Joe Corona headed down a Jose Torres cross.
Wondolowski, who produced the perfect riposte to having his name misspelled on his shirt, 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 Juergen Klinsmann's team, who are looking for their fifth Gold Cup title.
In the early Group C encounter at the same Jeld-Wen Field venue, midfielder Michael Barrantes scored twice as Costa Rica comfortably beat Cuba 3-0.
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 the referee spotted Jairo Arrieta inside the area 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 game was put well beyond a struggling Cuba when Barrantes virtually passed the ball into the net, from 20 yards out, beating the slow-reacting keeper Odelin Molina.