New Zealand were bowled out for 171 with just three balls remaining and just shy of their target of 174, with Rubel taking the final wicket when he bowled Kyle Mills in a dramatic finish at the Sher-e-Bangla Stadium.
Rubel finished with four for 25 — his best figures in limited-overs internationals — as Bangladesh successfully defended what was a meagre total.
It was the fifth and final one-dayer of the series. One match was rained off.
Rubel removed dangerman Brendon McCullum and helped reduce New Zealand to 20-5 with his fierce opening spell of 3-13 before Daniel Vettori and Grant Elliott put on 86 for the sixth wicket.
Vettori, the New Zealand captain, made 43 and Elliott top-scored with 59 as the tourists recovered before the momentum shifted back.
Captain Shakib Al Hasan had earlier top-scored for Bangladesh with 36 off 47 balls. Opener Imrul Kayes made 34 as the home side were bowled out in 44.2 overs.
Vettori took 3-32 and Mills 3-36.
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