Bangladesh captain Habibul Bashar admitted his side had wasted a good chance to give New Zealand a close game in Chittagong.
Having bowled out the tourists for 224, the Tigers could only make 86 in reply in the first of three one-day games.
"It was a disappointing batting performance," said Bashar.
"Our bowlers did well to restrict them, but we could not bat well. We lost too many early wickets. We hope to do better in the remaining two matches."
New Zealand were in trouble at 94-5 but Chris Cairns (74) put together a 49-run partnership with Scott Styris (43) for the sixth wicket to boost the total.
Kyle Mills took 4-14 and Black Caps captain Daniel Vettori 3-9 as Bangladesh crumbled to lose by 138 runs.
"The pitch was pretty tough for batting," said Vettori.
"We were lucky to reach 224 as Styris and Cairns were involved in a valuable stand. We hope the wicket will be better in the next game."
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After bowling New Zealand out for 225 within 50 overs for once I thought we had a match on our hands
