Group B, Kimberley. New Zealand 199-3 (33.3 overs) beat Bangladesh 198-7 (50 overs) by seven wickets
New Zealand raced to their third consecutive win at the expense of a much improved Bangladesh side on Thursday.
The Black Caps reached the easy target of 199 in less than 34 overs to keep their Super Sixes ambitions very much alive.
Opener Craig McMillan smashed 75, before some heavy hitting from Chris Cairns (33) and Scott Styris (37) guided New Zealand home with a much-needed boost
to their run-rate.
But their emphatic win could not take away from the plucky display by their opponents, who produced their best performance in the tournament so far.
Mohammad Ashraful hit a career-best 56 as Bangladesh scored their highest innings total at this World Cup and batted for the full 50 overs for the first time in South Africa.
The Kiwis finally restricted the Tigers to 198 for seven as all-rounder Jacob Oram and paceman Shane Bond finished with three wickets apiece.
A late flurry of boundaries from Mohammad Rafique (41) and captain Khaled Mashud (35) allowed Bangladesh to leave their innings on a high as the pair shared an unbroken eighth-wicket stand of 70 - a record for the bottom-of-the table team.
Knowing that a good run-rate was essential, captain Stephen Fleming led the Kiwi batting assault with a quickfire 32 before becoming the first of seamer Khaled Mahmud's three victims in the afternoon.
McMillan took up the chase, helped by an 18 from Andre Adams, before being bowled behind his legs by Mahmud.
Cairns then came to the crease and put on a devastating display with Styris, hitting his 33 from 21 balls and smashing one six clean out of the ground.
Their impressive performance ensured a speedy victory in a match where acquiring a good run rate was just as important as winning.
Resuming their World Cup campaign 10 days after beating hosts South Africa in Johannesburg, the Black Caps had been given a reminder of the importance of their Group B match by the unlikeliest of sources.
African minnows Kenya threw the group wide open on Monday with their shock victory over former World Cup winners Sri Lanka.
New Zealand: Stephen Fleming (captain), Craig McMillan,
Mathew Sinclair, Scott Styris, Chris Cairns, Brendon McCullum,
Jacob Oram, Kyle Mills, Andre Adams, Daniel Vettori, Shane Bond.
Bangladesh: Khaled Mashud (captain), Hannan Sarkar, Habibul
Bashar, Sanwar Hossain, Alok Kapali, Mohammad Rafique, Tapash
Baisya, Manjurul Islam, Mohammad Ashraful, Khaled Mahmud, Akram
Umpires: David Shephered (Eng), Darrell Hair (Aus)
TV umpire: Brian Jerling (Rsa)
Match referee: Mike Procter (Rsa)