Italy had initially led 3-1 but Hungary overturned that to take a 5-4 advantage before the Italians pulled clear.
Hosts Greece stunned third-ranked Russia with a 7-4 victory and they now face Australia in the last four.
Antigoni Roumpesi scored two goals in the second period, while Kyriaki Liosi added two more in the third.
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MMIX
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The defining images