First half goals from Luton Shelton and Ryan Johnson were supplemented after the break by Demar Phillips and Keammar Daley efforts as Jamaica dominated their opponents in an opening Group B match that could have been much worse for Grenada.
"Our finishing was a big letdown," Jamaica manager Theodore Whitmore told reporters after his team recorded 10 shots on goal. "We managed to score four - what a way to start."
Grenada, the smallest nation competing in the 12-nation tournament for North and Central America and the Caribbean, have yet to record a Gold Cup goal after being outscored 10-0 in their first tournament appearance in 2009.
Grenada goalkeeper Shemel Louison made some daring saves in the second half, but his team managed just one wayward attempt at goal and could not keep Jamaica from dominating possession.
Johnson, who plays for the San Jose Earthquakes in Major League Soccer, was named the man-of-the-match as he helped his side thrive even without forward Omar Cummings, who missed the game with an ankle injury.
"I want to help Jamaica go as far as we can in this tournament," Johnson said. "We did the most important thing, and that was to keep a clean sheet.
Both teams resume Group B action on Friday in Miami, where Jamaica face Guatemala and Grenada take on Honduras.
