New Zealand chased down a mediocre target of 132 with more than 28 overs to spare with Henry Nicholls not out 49 and debutant Will Young on 11 at the close.
But the early finish was set up by an aggressive start from opener Guptill who blazed away for 38 off 19 deliveries.
All but two of his 38 runs came from boundaries with four sixes and three fours before Taskin Ahmed found a faint edge and wicketkeeper Mushfiqur Rahim completed the dismissal.
New Zealand win! Brilliant bowling from the @BLACKCAPS helps the hosts to an eight-wicket victory over @BCBtigers… https://t.co/EwduSBoHxK
— ICC (@ICC) 1616210646000
The quickfire opening put Bangladesh on the back foot with Nicholls untroubled as he picked off the bowlers, only to be denied his 12th half century by Young who brought up the winning runs with a boundary.
In the first clash in a three-match series, New Zealand won the toss and elected to bowl with captain Tom Latham correctly predicting that if there was anything in the wicket it would be early in the day.
Bangladesh opener and skipper Tamim Iqbal looked to dominate with a six off Boult’s third ball and a four off the second over from Matt Henry.
Bangladesh lost by 8 wickets in the first ODI.#BANvNZ #RiseOfTheTigers https://t.co/iN5RmCDvMq
— Bangladesh Cricket (@BCBtigers) 1616211321000
But on a ground where the average winning score is in excess of 300, the tourists were soon in trouble when Boult took two wickets in his third over.
He started with the dismissal of Iqbal, trapping him lbw with a straight delivery as the Bangladesh skipper waited for the ball to swing.
New batsman Soumya Sarkar went three balls later without scoring and Bangladesh never recovered.
Boult later removed Taskin Ahmed (10) and Hasan Mahmud (one) to finish with four for 27.
Liton Das (19) and Mushfiqur Rahim (23) stayed together for nearly nine overs but added only 23 runs before both were removed by Jimmy Neesham.
Neesham was central to a third wicket when he spilled a return chance from Mahmudullah only for the ball to deflect on to the stumps and run-out non-striker Mohammad Mithun who was backing up too far.
Neesham took two for 27, left-arm spinner Mitchell Santner took two for 23 while the economical Henry dismissed Mahmudullah, Bangladesh’s top scorer, for 27.
The second match in the three-match series is in Christchurch on Tuesday.