Marco Urena scored a goal in each half to give the Ticos the lead in the seventh minute. Alvaro Saborio, Heiner Mora and Joel Campbell also scored for Costa Rica, which has won all four matches against Cuba in the Gold Cup.
With the win, Costa Rica improved its record against Caribbean teams at the regional tournament with a 10th win in 16 matches.
Cuba remained winless against Central American teams and also extended its winless skid to eight in the Gold Cup, having lost seven of those since a 2-0 win over Canada 2-0 at the 2003 Gold Cup.
Today, Jamaica takes on Grenada while Honduras faces Guatemala.
Cuba and Costa Rica play next on Thursday at the Bank of America Stadium in Charlotte, North Carolina. Costa Rica plays El Salvador, followed by Cuba taking on Group A favorite Mexico in the second game of the doubleheader.