Bangladesh's Mushfiqur Rahim is run out by New Zealand's Tom Latham during the match on Wednesday. Reuters
Bangladesh was all out for 244 after New Zealand won the toss and put the squeeze on at the Oval in their day-night match.
The top five batsmen all made starts but invariably got themselves out under pressure to escape New Zealand's grip.
Shakib Al Hasan, the third Bangladeshi to play 200 ODIs, top scored with 64. He was the only batsman to score more than 30.
The New Zealand battery, backed up by smart fielding, took advantage of a fresh pitch, overcast skies, and disciplined bowling to set a gettable target.
Matt Henry returned 4-47 and Trent Boult snared a pair of wickets, while Lockie Ferguson, Colin de Grandhomme, and Mitchell Santner took one each.
Santner, the slow left-armer, was unhittable through the middle overs, not conceding a boundary until his ninth over, and the only six of the match in his 10th. But his performance will also have heartened the Bangladesh spinners.
New Zealand has a 4-0 win record against Bangladesh at the World Cup, batting second each time.
Sri Lanka started the tournament as rank outsiders and finished sixth of the nine teams, registering one of their three wins against the world's top-ranked one-day international side and hosts England.
A throw to the stumps deflected off the bat of a diving Ben Stokes as he tried to complete a second run and raced to the boundary, with Sri Lankan umpire Kumar Dharmasena awarding six.
Sarfaraz Ahmed's side needed to smash the world record for margin of victory in a one-day international but, after winning the toss at Lord's, they failed to muster enough runs to give them a chance.
Bangladesh must be all out for seven or lower if Pakistan are to deny New Zealand a place in the semi-finals alongside Australia, India and England.
The broadcaster said their decision would "ensure as wide an audience as possible is able to watch the game."
England have qualified for the semi-finals and will meet either India or Australia on Thursday July 11. The final is at Lord's on July 14.
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