The first match was washed out and Bangladesh made four changes from the team which lost the second game on Saturday by 86 runs.
Bangladesh stand-in captain Najmul Hossain made a brilliant 76, his third straight 50-plus knock but other batters failed to support him. The next best was Mahmudullah’s 21.
Aiming to draw the series, Bangladesh quickly lost both openers Tanzid Hasan and Zakir Hasan. That left the hosts at 8-2 in the third over. Zakir made just 1 before Milne rattled his stumps with an express delivery. Trent Boult (2-33) claimed Tanzid’s wicket.
Towhid Hridoy looked confident but Milne had him caught by Young at point to dismiss him for 18. Mushfiqur Rahim scored 18 before falling to skipper Lockie Ferguson.
Mahmudullah hit leg-spinner Ish Sodhi for consecutive boundaries but he too failed to convert his start as he edged behind after sharing a 49-run for the fifth wicket with Najmul.
After becoming the first New Zealand spinner to claim six wickets in a one-day international, Sodhi went wicketless in this match.
Najmul kept the scoreboard ticking but Bangladesh lost the last five wickets for just 34 runs. He was out when trying to play a reverse sweep against offspinner Cole McConchie (2-18 in five overs). Najmul struck 10 fours in his 84-ball knock.
In reply, New Zealand’s Finn Allen hit three boundaries in the first over against left-arm pacer Shoriful Islam (2-32). Young also regularly hit boundaries as the Kiwi openers made a good start, unlike Bangladesh.
But Shoriful hit back with consecutive wickets, removing Allen for 28 and handing Dean Foxcroft a golden duck on his debut.
Young and Nicholls then combined for an 81-run stand for the third wicket.
Left-arm spinner Nasum Ahmed broke the partnership, claiming Young after he hit 10 fours and one six in his knock.
Tom Blundell (23) hit the winning boundary.
Liton Das, who led Bangladesh in the first two matches, was rested along with Tamim Iqbal, Soumya Sarkar and Mustafizur Rahman.
