Haiti levelled in the 57th minute through Duckens Nazon's penalty and the 21-year-old Alexis completed the comeback with less than 10 minutes left, rifling the ball home from close range after good work on the left by Derrick Etienne and Alex Christian.
Haiti celebrated wildly, with Alexis running into the arms of his coach and team mates on the sidelines.
While both teams had already secured spots in the quarter-finals, the Haitians' win sees them face Canada on Saturday in Houston, while Costa Rica take on Mexico.
(Writing by Jahmal Corner in Los Angeles; Editing by Peter Rutherford)
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