It left Glenn Phillips and Michael Bracewell to calm any late nerves, seeing the Black Caps home with 3.5 overs to spare and securing a win that also meant India progressing into the last four, while Bangladesh and Pakistan bowed out.
Rachin Ravindra steered New Zealand into the Champions Trophy semi-finals after hitting his fourth ODI century in a five-wicket victory over Bangladesh.
Bracewell earlier played a key role with the ball after Bangladesh finished on 236 for nine following New Zealand’s decision to field first.
His four for 26 was the best return by a New Zealander in Champions Trophy history as he removed four of Bangladesh’s top-six batters.
Their 129-run partnership moved the game away from Bangladesh, and the job was almost done when Ravindra holed out in the deep off Rishad Hossain’s bowling.