Substitute Al Hammadi latched on to a through pass before slotting it home after regulation time had ended 1-1.
UAE drew first blood just before the half-hour mark when Umar Abdul Rahman rounded four Iraqi defenders before unleashing a left-footer to put his team ahead.
Iraq equalised through striker Younis Mahmoud with less than 10 minutes to go to force extra time but could not deny UAE their second Gulf Cup title.
Earlier, Kuwait thrashed 10-man Bahrain 6-1 to finish third.
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