It was only the third hat-trick in the history of Twenty20 internationals as a withering Southee spell put the brakes on a brisk Pakistan start from which the tourists never recovered.
Their 143 for nine was knocked off by New Zealand with 17 balls to spare and five wickets in hand, giving the Black Caps a much-needed victory after a string of 11 one-day defeats.
"After the way we've played in the last three-four months it's a great start" to the Pakistan series, said stand-in captain Ross Taylor as he congratulated man-of-the-match Southee.
"Tim was outstanding."
It was also a morale-boosting performance for new coach John Wright who was only brought in to guide the team in a major shake-up last week and was immediately confronted with the news his most senior players Daniel Vettori and Brendon McCullum were out injured.
New Zealand's poor run appeared to be continuing when Pakistan raced to 62 for two in a rollicking first seven overs before Southee turned the game around in a whirlwind nine-ball spell in which he took five wickets for no runs.
It began with the last ball of his opening over when he had Ahmed Shehzad caught by wicketkeeper Peter McGlashan for 14.
With the second ball of his next over he seduced Younis Khan (two) with a widish delivery that was top edged to debutant Dean Brownlie in the deep.
As the ball was skied, opener Mohammad Hafeez was left to regret racing to the other end as his innings of 24 off 19 deliveries ended on the next ball which he nicked to McGlashan.
Umar Akmal was unfortunate to complete the hat-trick when given out leg before wicket on the first ball he faced as television replays indicated a thick inside edge before the ball hit the pads.
Southee rounded off his wicket-taking exploits with the second ball of his third over which Abdul Razzaq (one) steered to McGlashan and he ended his four-over spell with the impressive figures of five for 17.
Kyle Mills, who finished with three for 37 continued to keep the pressure on Pakistan who were in danger of not batting through their innings before the tail-end pair Wahab Riaz and Shoaib Akhtar piled on an unbeaten 31 in the last two overs.
But 143 was never going to be enough on an easy surface and New Zealand openers Jesse Ryder and Martin Guptill took control from the start.
They had 27 runs on the board inside two overs before Ryder (six) departed as the first of Akhtar's three wickets.
Brownlie (five) and Scott Styris (seven) also fell cheaply to the express bowler but New Zealand always had the run rate under control.
Guptill blasted 54 from 29 balls, including four sixes and four fours, before he was run out while Taylor was 39 not out from 31 balls at the end.
New Zealand lead the three-match series 1-0 with the second match in Hamilton on Tuesday.