The Cubans took the early lead when Jose Ciprian Alfonso scored in the 21st minute off a volley but Panama replied with six goals of their own to advance to the semi-finals against either Mexico or Trinidad and Tobago.
Gabriel Torres scored twice, including a penalty, in the first half as Panama quickly recovered to lead 2-1 at the break.
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.