New Zealand came up against stern defence from the previously overwhelmed Cook Islands and could only win 2-0 in Alabny.
The home team were expected to boost their goal difference against a side who had ost its previous matches in the Oceania group two section by 9-1 and 8-1.
Although the New Zealand team launched several shots at the Cook Island's goal but goalkeeper Tony Jamieson was excellent and he was only beaten in the second half.
Noah Hickey scored with a header from a cross by substitute Arran Lines in the 65th minute and scored with a low drive less than a mnute later.
Earlier the Solomon Islands hammered Vanuatu 7-2 to send them top of the group on goal difference ahead of their decisive game against New Zealand on Monday.
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