Martinique, who suffered a 4-0 defeat to Canada in their Group A opener last Saturday, went ahead in the 45th minute when Marveaux headed in from a corner.
Both teams had chances in a first half that was a battle of the goalkeepers but Martinique seized control after the break and could have added to their lead in the 59th minute had Mickael Biron's penalty not sailed above the crossbar.
An Abaul header off another corner secured Martinique's second goal in the 70th minute while Fortune put the game away 15 minutes later when he slotted from in close shortly after Cuba's Erick Rizo was sent off.
Cuba had plenty of chances but could not convert and bow out following a 7-0 drubbing by Mexico in their opener.
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Group A action resumes on Sunday in Charlotte, North Carolina, where Martinique will face seven-time Gold Cup champions Mexico after a clash between Cuba and Canada.
(Reporting by Frank Pingue in Toronto; Editing by Ian Ransom)
