Chasing 144 for victory, the Blacks Caps reached 146 for five with 17 balls to spare.
The result at Eden Park in the first of three T20 matches between the sides marked a winning start for the home side under new coach John Wright.
Their run chase was founded on some big hitting from Guptill, who scored 53 off 28 balls, blasting four fours and four sixes.
Skipper Ross Taylor added an unbeaten 39 which included two fours and three sixes.
Earlier pace bowler Southee grabbed a hat-trick today as New Zealand held a fast-starting Pakistan to 143 for nine.
The hat-trick came in a nine-ball stretch spread over three overs in which Southee took five wickets without conceding a run, helping to reduce Pakistan from 58 for one to 70 for six at Eden Park.
With the visitors travelling at 10 runs an over during the first five overs after being sent in to bat, Southee's first scalp came when he had Ahmed Shehzad caught by wicketkeeper Peter McGlashan.
In successive balls in his next over, Younis Khan was caught by debutant Dean Brownlie, opener Mohammad Hafeez edged to McGlashan and Umar Akmal was dismissed leg before.
On a pitch offering bounce, the Northern Districts seamer completed his five-wicket bag by having Abdul Razzaq caught behind.
His haul of five for 18 from his four overs saw him elected as man of the match.
Kyle Mills chimed in with three for 37, but teenager Adam Milne, the other New Zealander handed his debut, had a tough introduction, finishing with 0-46 although he did show plenty of pace.
Milne also dropped Hafeez on the third-man boundary off Mills' bowling with the score at 36-0, although Mills got the opening wicket a ball later when skipper Shahid Afridi lofted a catch to Southee at mid-on.
Umar Gul, 30, and Wahab Riaz, 30 not out, top-scored to give the Pakistan innings some late impetus.
New Zealand also made a quick start to their chase, with Guptill producing some big hitting.
He saw fellow opener Jesse Ryder, six, Brownlie, five, and Scott Styris, seven, depart cheaply, all to veteran paceman Shoaib Akhtar, who showed he still had plenty of speed.
But Guptill keep the runs flowing at his end before he was run out when sent back by Taylor after considering a quick single, to leave the score at 91 for four.
With more than half their overs still available, the Black Caps had few real scares before getting home.
The second match of the series is in Hamilton on Tuesday.
Taylor said it felt pretty good to start the series off with a win, particularly after the way they had played in the last three or four months.
"There are some good signs there and I am sure we learned a lot from today."
Guptill had stood out with his batting and Southee had bowled very well in the middle section of the Pakistan innings while getting able suport from Scott Styris.
"It has been good to finish it off with a win today."
Pakistan skipper Shahid Afridi said his side were looking for a score of between 160 and 165 but Southee had bowled well.
"I feel the guys got out to some bad shots as well . . . ."
"There's a lot to work on but we will play differently in the next game (at Hamilton on Tuesday).
Pakistan
M Hafeez c McGlashan b Southee 24; S Afridi c Southee b Mills 20; A Shehzad c McGlashan b Southee 14; Y Khan c Brownlie b Southee 2; F Alam c Franklin b Styris 9; U Akmal lbw b Southee 0; A Razzaq c McGlashan b Southee 1;U Gul lbw b Mills 30; W Riaz not out 30; S Ajmal c McGlashan b Mills 1; S Akhtar not out 8; Extras (1lb, 3w) 4; Total (for 9 wkts, 20 overs) 143.
Fall: 37, 58, 62, 62, 68, 84, 110, 112.
Bowling: J Franklin 2-0-12-0 (1W), K Mills 4-0-37-3, A Milne 4-0-46-0, T Southee 4-1-18-5 (1W), S Styris 4-0-18-1 (1w), N McCullum 2-0-11-0.
New Zealand
J Ryder c Khan b Akhtar 6; M Guptill run out 54; D Brownlie c Akmal b Akhtar 5; S Styris b Akhtar 7; R Taylor not out 39; J Franklin lbw b Hafeez 19; P McGlashan not out 5; Extras (4b, 1lb, 6w) 11; Total (for 5 wkts, 17.1 overs) 146
Fall: 27, 45, 55, 91, 115.
Bowling: A Razzaq 1-0-15-0, S Akhtar 4-0-38-3, U Gul 2-0-16-0 (1w), S Ajmal 3.1-0-14-0, W Riaz 1-0-10-0, S Afridi 3-0-19-0, M Hafeez 3-0-29-1 (3w).
Result: New Zealand won by five wickets.
