Bangladesh set New Zealand 266 for victory on Thursday after Shanto's patient 105 and Litton Das's fluent 76, and while the Black Caps overcame some initial turbulence to get into a strong position in their chase, they were eventually bowled out for 210 in 44.5 overs.
Nick Kelly gave the tourists hope, scoring 59, but he perished chasing a slow, wide ball from Rahman (5-43), and the Bangladesh seamer ran riot from there to ensure his team's victory despite late fireworks from Dean Foxcroft's 75.
New Zealand struck early after winning the toss and asking Bangladesh to bat, as Will O'Rourke (3-32) sent back opener Saif Hassan for a two-ball duck and got Tanzid Hasan to play one onto his stumps in the third over.
The paceman similarly bowled out Soumya Sarkar for 18 to leave Bangladesh in trouble at 3-32, but the hosts fought back through a 160-run partnership between Shanto and Das when New Zealand's bowlers went off the boil slightly.
That fourth-wicket stand was broken by Jayden Lennox (2-50) when he bowled Das, before Shanto scored his first ODI century since 2024 and then departed while looking to raise the scoring rate with seven overs remaining.
Bangladesh finished on 8-265 after handy knocks from Towhid Hridoy (33) and Mehidy Hasan Miraz (22), while Ben Lister (2-62) claimed late wickets to keep things in check.
New Zealand won the series opener by 26 runs in Mirpur and the hosts levelled at 1-1 with a six-wicket victory at the same venue on Monday.
The teams play three Twenty20 Internationals starting in Chattogram next week.
