Neesham became the fourth New Zealander - after Tim Southee, Lockie Ferguson and Adam Milne - to take five wickets in a T20 international as the Black Caps restricted Pakistan to 9-128 after winning the toss on Wednesday.
Seifert and Finn Allen then launched New Zealand's run chase at an astonishing pace, rushing to 0-45 after three overs, to 50 from 22 balls and finally to 0-82 at the end of the six-over power play.
While Allen was left almost a spectator, Seifert raced to his 10th T20 half-century from 23 balls, with five sixes and five fours. The pair put on 93 for the first wicket in 6.2 overs before Allen was out for 27 from 12 balls.
Seifert carried on at an unbroken pace, hitting 10 sixes and six fours and finishing the New Zealand run chase with four sixes in the 10th over.
"After I nearly got hit in the head by that first ball, I thought there's only one way to play," Seifert said.
"The wickets were very bouncy and to be able to play as I wanted to play is the thing I'm most proud of."
In contrast, Pakistan were 3-27 after the power play and 4-52 at the mid-point of their innings, struggling against the bounce produced by the New Zealand bowlers.
Opener Hasan Nawaz was out for a duck, continuing an extraordinary start to his international career. In his five T20 matches so far, he has made 0, 0, 105 not out, 1 and 0.
Captain Salman Ali Agha made 51 from 39 balls and put on 54 for the sixth wicket with Shadab Khan, who hit 28 from 20 balls.
Shadab was out in contentious circumstances. Neesham lost control of the first ball of the 17th over which the umpire ruled was four wides. Shadab believed and replays suggested the ball had missed the pitch and therefore was a no-ball.
He was out from the next ball which, if a no-ball had been called, would have been a free hit from which he could not have been dismissed.
