Bangladesh rode on a brilliant innings by Mahmudullah, who starred in two crucial partnerships with Soumya Sarkar (51) and Sabbir Rahman (40) for the third and sixth wicket respectively after Kiwi skipper Brendon McCullum won the toss and elected to field.
Mahmudullah, who had become the first Bangladesh batsman to score a World Cup century during his 103-run innings against England on Monday, shared 90 runs with Soumya before adding another 78 with Sabbir today.
The 29-year-old cracked 12 boundaries and three sixes in his 123-ball unconquered innings at Seddon Park. Soumya had seven boundaries to show in his 58-ball stay, while Shabbir blasted five fours and two sixes in his 23-ball innings.
For New Zealand, Corey Anderson (2/43), Trent Boult (2/56) and Grant Elliott (2/27) scalped two wickets each, while Daniel vettori claimed one.
Bangladesh lost both their openers inside 10 overs with the score reading 27 for two but Mahmudullah and Soumya stemmed the rot with a 90 run partnership as the Asian nations crossed the 100-mark.
Soumya threw his wicket just after amassing his fifty when he caught by Anderson at long-on off Vettori.
Shakib Al Hasan (23) and Mahmudullah then brought up the 150 before Anderson got rid of the Bangladeshi allrounder as they slipped 151-4 in 34 overs.
Mushfiqur Rahim (15) too had a brief stay in the middle and after he was dismissed by Anderson it was Sabbir, who played the perfect cameo to raise the tempo after the 40th over.
Sabbir and Mahmudullah ensured Bangladesh accumulated 108 runs in the last 10 overs as they took the attack to the opposition, adding 78 off 48 balls, to take their team across the 250-mark.