Southee claimed five wickets in a period of eight balls, finishing with 5-17 — the first five-wicket bag by a New Zealander in Twenty20 internationals — as New Zealand held Pakistan to 143-9 after winning the toss.
Guptill then made 54, including a 23-ball half century - the fastest by a Kiwi in Twenty20s - to guide New Zealand to victory with 17 balls to spare.
Southee set up the win, which puts New Zealand 1-0 up in the three-match series, with an outstanding spell of swing bowling.
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.
Khan was caught in the deep by Dean Brownlie who, with 18-year-old fast bowler Adam Milne, was one of two players to make their debuts for New Zealand at Eden Park on Sunday.
Hafeez was caught by Peter McGlashan, who took over the wicketkeeping duties from the injured Brendon McCullum and claimed four catches, becoming only the seventh player to do so in Twenty20 internationals.
Southee completed his hat trick when he trapped Umar Akmal lbw.
“It wasn't too bad,” Southee said. “It was one of those days when everything went my way. It was a good pitch and if you hit the right areas you got rewarded but if you missed you got hit.” When Southee dismissed Abdul Razzaq (1) with the second ball of his third over, he had taken five wickets for seven runs and Pakistan, which had been 37-1, was 68 for 6.
Umar Gul and Wahab Riaz shared Pakistan's top score of 30 to revive the innings.
Guptill put New Zealand on the way to a comfortable win when he hit four fours and four sixes to rush his half century. He beat the record for the fastest half-century in Twenty20s for New Zealand held by Aaron Redmond.
Guptill was finally run out for 54, having backed up too far, but captain Ross Taylor, standing in for the injured Daniel Vettori, guided New Zealand home with an unbeaten 39.
The victory gave New Zealand unaccustomed success after it recently extended its losing streak in one-day internationals to 11 matches with a 5-0 series loss in India.
“I guess anytime you start a series with a win, and with the way we've played in the last three or four months, it's a good feeling,” Taylor said.
Pakistan captain Shahid Afridi said his team would improve as it acclimatized to New Zealand conditions.
“I think the way we started we should have scored 160 or 165,” he said “But Southee bowled really well, he put it in the right areas and we played some bad shots.” The second match of the series is scheduled for Hamilton on Tuesday.
