Opener Martin Guptill hit a fighting century to guide New Zealand to their sixth consecutive victory in the World Cup with a three-wicket win over an inspired Bangladesh in Hamilton on Friday.
Earlier, Mahmudullah, dropped on one by Anderson off Southee, anchored the innings and added an invaluable 90 for the third wicket with Soumya Sarkar (51) and another 78 for the sixth with Sabbir Rahman who made a fiery 23-ball 40.
Rahman raised the tempo by hitting two sixes and five fours to help Bangladesh add 104 runs in the last ten overs.
Left-arm paceman Trent Boult had jolted Bangladesh by dismissing Imrul Kayes (two) and Tamim Iqbal (13) in his first spell to finish with 2-56.
Anderson removed senior Bangladeshi batsmen Shakib A Hasan for 23 and Mushfiqur Rahim for 15 to finish with 2-43.
Bangladesh caught New Zealand napping at 33-2 by taking the key wickets of Brendon McCullum (eight) and Kane Williamson (one) by opening with spin from both ends — only the second time in World Cup history when slow bowlers opened the attack.
Left-arm spinner Shakib Al Hasan took both the early wickets before Guptill and Ross Taylor (56) revived the innings through their 131-run stand for the third wicket.
Taylor, who hit five fours, added another 46 with Grant Elliott (39) before Bangladesh took three wickets in the space of 37 runs to get a sniff of an upset victory.
Corey Anderson, who hit three fours and as many sixes, fell for 39 before Tim Southee hit a six and a four to seal New Zealand's first win after seven successive defeats against Bangladesh between 2010-2013 — all away from home.
New Zealand had already made sure of top spot in Pool A and they will face the fourth-placed finishers from Pool B — where Pakistan, Ireland and West Indies are still alive — in the fourth quarter-final in Wellington on March 21.
Bangladesh, who finished the group stage with seven points from six matches, will face defending champions India in the second quarter-final in Melbourne on March 19.
