Gabriel Torres scored twice, including a penalty, in the first half as Panama quickly recovered to lead 2-1 at the break.
His fellow striker Blas Perez also netted two goals, both in the second half, while defender Carlos Rodriguez and substitute Jairo Jimenez each scored once.
Cuba only scraped into the quarter-finals after an injury time goal in their last group match.
Mexico were due to face Trinidad and Tobago later on Saturday in Georgia. The other two quarter-finals will be held in Baltimore on Sunday with the winners advancing to Wednesday's semi-finals in Texas.
(Reporting by Julian Linden in New York; Editing by Gene Cherry)
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