New Zealand have scored 239 runs by losing seven wickets against Bangladesh at University Oval, Dunedin on Sunday.
Light rain pushed back the 1100 (2200GMT) start, causing the match to play for 30 overs each innings.
Bangladesh won the toss and chose to bowl in the first. Skipper Najmul Hossain Shanto said he hoped his bowlers could capitalise on overcast conditions.
Shanto wants to end his team's dire 50-over record in New Zealand, where they have lost all 16 ODI matches against the hosts.
"The boys are very excited, including some of the new boys in the squad. We hope we can do better in this series," he said.
New Zealand captain Tom Latham said he would have also bowled first if he had won the toss.
"It looks a decent surface," he added. "So, it's a good opportunity to start the summer by putting some runs on the board."
New Zealand: Will Young, Rachin Ravindra, Henry Nicholls, Tom Latham (capt), Tom Blundell, Mark Chapman, Josh Clarkson, Adam Milne, Ish Sodhi, Jacob Duffy, William O'Rourke.
Bangladesh: Najmul Hossain Shanto (capt), Litton Das, Anamul Haque, Towhid Hridoy, Afif Hossain, Mushfiqur Rahim, Mehidy Hasan Miraz, Mustafizur Rahman, Soumya Sarkar, Hasan Mahmud, Shoriful Islam.
Bd-pratidin English/Tanvir Raihan
