Antony Lozano got one back for Honduras nine minutes into the second period but Damion Lowe, with a powerful header from a corner, restored Jamaica’s two-goal cushion two minutes later.
Honduras substitute Rubilio Castillo got his side's second in stoppage time but it was too little too late as Jamaica, runners-up at the last two Gold Cups, collected three points in their Group C opener.
El Salvador beat Curacao 1-0 earlier on Monday in the other group game.
Both matches were held at Kingston’s Independence Park as part of the Gold Cup's expanded 2019 tournament.
In addition to increasing the number of teams taking part in this year’s tournament to 16 from 12, the confederation decided to stage games in Jamaica and Costa Rica as well as in the United States.
Jamaica’s next match is against El Salvador in the first of a double header in Houston on Friday, with Honduras taking on Curacao later the same day.
(Reporting by Andrew Downie; Editing by Peter Rutherford)
