Blas Perez, Luis Tejada and Gabriel Gomez scored for Panama to hand the side the win.
The victory was only Panama’s second in its last eight Gold Cup matches and avenged a 2-1 loss to the French Caribbean island two years ago in the opening round of the tournament.
The Panamanians next face the United States in Tampa on Saturday. Guadeloupe takes on Canada.
Meanwhile, the U.S. whipped Canada 2-0 Tuesday night. Jamaica beat Grenada 4-0 Monday night while Honduras played to a 0-0 tie with Guatemala.
Tomorrow, Costa Rica plays El Salvador and Cuba takes on Mexico at 7 and 9 p.m., respectively.