Southee claimed all five wickets in a period of eight balls at Eden Park, becoming the first New Zealander to take a five-wicket bag in Twenty20 internationals.
He dismissed Ahmed Shahzad (14) with the last ball of his first over, then completed a hat trick when he removed Younis Khan (2), Mohammad Hafeez (24) and Umar Akmal (0) with the second, third and fourth deliveries of his second over.
When he dismissed Abdul Razzaq (1) with the second ball of his third over, Southee had five wickets for seven runs and Pakistan was 68 for 6.