Bangladesh won their first ever match in New Zealand and took a psychological edge for the one-day series, beating a New Zealand XI in their Twenty20 match.
Shahadat Hossain took 3-15 for the tourists
The home side, including five one-day squad members and five on the fringes, fell by four wickets in Hamilton.
James Marshall hit 33 off 26 balls, while Scott Styris scored 29 as the hosts made 133-7 off their 20 overs.
After a tough start, Farhad Reza hit 31 off 17 balls and Mushfiqur Rahim scored the winning run in the 17th over.
Previously on this tour, Bangladesh had lost one-day matches to a Northern Districts provincial side and to Auckland.
They failed to achieve a win in any form of the game on their first two tours to the country.
However, the New Zealand XI struggled throughout their 20 overs after they were sent in to bat.
Tigers opening bowler Shahadat Hossain returned 3-15 off his four overs.
Bangladesh made easy work of the run chase, although Saqibul Hasan and Shahadat Hossain both made 22, while both Mohammad Ashraful and Aftab Ahmed were run out for 20.
The match was played to help raise money for World Vision's relief fund to alleviate the damage suffered in Bangladesh from Cyclone Sidr in November.
International Cricket Council chief executive Malcolm Speed presented the team's management with a cheque for US$250,000 [£126,000] before the match.
The first game of the three-match one-day series is on Wednesday at Eden Park in Auckland before the series moves to Napier and Queenstown.
The two sides will then play a two-match Test series.