The former captain finished 60 not out from 56 balls with just six fours, with wickets falling around him as New Zealand failed to build on a second-wicket stand of 133 between skipper Tom Latham and Neil Broom.
New Zealand broke through with wickets to Patel, Hamish Bennett (1-47) and Mitchell Santner (1-53) but a key unbeaten partnership between Mushfiqur Rahim (45no) and Mahmudullah (46no) steered Bangladesh home.
Luke Ronchi lasted only five balls after Bangladesh won the toss with Mustafizur Rahman breaching his defence in the second over.More news: Trump urges grads to draw lessons from his outsider status
Bangladesh are heading into the match high on confidence after decimating Ireland in their penultimate tie of the series by eight wickets. Although Bangladesh did not take a wicket for 24.3 overs, they did however create opportunities, but squandered both of them.
New Zealand, meanwhile, will look to continue their dominance over lower-ranked sides.
Latham, who reached his fifty off 51 deliveries was handed another reprieve when Mosaddek Hossain (0-14) off his own bowling in the 15th over and at the halfway mark, New Zealand were placed comfortable at 134 for one.More news: Britain Raises Terror Alert to Critical - the Highest Level
Captain Latham top-scored for the third successive Black Caps global, posting a patient 84 off 92 balls after his team were asked to bat.
New Zealand will want to stay unbeaten in the series keeping with their top-dog status among the three teams in the mix. They were the risky trio of Jimmy Neesham, Mitchell Santner and Colin Munro.
The match is being played at the Clontarf Cricket Club Ground, Dublin.More news: Kendall Jenner Wears Socks With Sandals on the Cannes Red Carpet
It was then Rubel's turn to show his expertise with fast, reverse-swinging yorkers - one of them bowling Matt Henry in 48th over - as Bangladesh conceded only 33 runs off the last five overs, most of the runs coming off Ross Taylor's bat. Mustafizur Rahman starred with four wickets as William Porterfield's men were bowled out for 181 after whcih Soumya Sarkar helped the Asians gun down the total in just 27.1 overs with a 68-ball 87.