In a physical contest, veteran Piquionne provided the difference, beating Cuban goalkeeper Odelin Molina after receiving a through ball from the influential Kevin Parsemain.
There was no shortage of opportunities, however, for the Lions of the Caribbean to get on the scoreboard. Alberto Gomez and Jaine Colome Valencia hit the crossbar in the first and second half, respectively.
Parsemain, though, was the game's outstanding performer. The 24-year-old forward, who scored six goals in a first-round win over the British Virgin Islands, was a creative force and his sharp skills continually challenged the Cuban defense. In the first half, he had an attempt knocked off the line by Jorge Corrales.
With 20 minutes remaining, Parsemain saw a 35-yard shot saved spectacularly by the outstretched Molina.
The victory extended Martinique's Caribbean Cup unbeaten streak to seven consecutive games.
Next up for Les Matinino is an encounter against Jamaica on Monday, while Cuba meets French Guyana.