Nagui netted with a fine curling shot from inside the box to give Egypt a record seventh title in the continental tournament.
Ghana, who were looking for their first Nations Cup title since 1982, defended neatly throughout but were helpless when Nagui raced into the box and unleashed the winner following a swift one-two.
Egypt, unbeaten in their last 19 Nations Cup games, were pipped by Algeria for a World Cup finals spot but they beat four World Cup-bound teams en route to their triumph.