Morgan led his side to their highest score against a top nation
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Ireland suffered another heart-breaking defeat and Scotland also continued their winless streak through the Under-19 World Cup consolation rounds.
Captain Eoin Morgan (124) led Ireland to 304-9 against New Zealand, their highest ever against a leading country.
But Tim Southee hit 92 from 55 balls as New Zealand, at one stage 150-4, won by three wickets with five balls to spare.
Scotland crashed to a 185-run defeat after South Africa posted 337-8, the highest total of the tournament so far.
However, both sides will continue in the Plate play-offs, with Ireland playing Namibia on Wednesday and Scotland facing Uganda on Friday.
Elsewhere, captain Hemant Punoo 2-36 and hit an aggressive 64 as USA won for the first time, beating Namibia by two wickets.