Martinique hit back with a double from Kevin Parsemain before Morris fired home the winner with a right-footed shot from the centre of the box in Tampa, Florida.
The win moved the United States joint top of Group B with Panama, who beat Nicaragua 2-1 on Wednesday, on four points.
Martinique, on three points, while face Panama on Saturday while the Americans take on Nicaragua, who have yet to claim a point.
(Writing by Jahmal Corner in Los Angeles; Editing by Peter Rutherford)
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