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Nazon gave Haiti the lead after 14 minutes, when he hit the back of the net after Kervens Belfort's assist.
Honduras came back into the match in the second half, but were unable to find an equaliser. Eddie Hernandez failed to hit the target with five attempts and Rubilio Castillo's shot was blocked with 20 minutes to spare.
A win for the USA against Panama later tonight would put Haiti through to the knockout stages.