But the game quickly slipped away. Bevon Jacobs turned it around with a blistering half-century, taking control of the chase when New Zealand were under pressure at 33 for 4.
Earlier, Bangladesh had collapsed dramatically after the rain break, bowled out inside 15 overs on a tricky surface that had variable bounce. Their total of 102 never quite felt enough.
New Zealand did wobble, but one solid partnership was all they needed. Jacobs made sure of that, guiding his side home and sealing a 1-1 series result.