Georgia Plummer smashed an unbeaten 41 off 22 balls, including seven fours, while Anna Browning made 28 not out as the target was reached in the eighth over.
The win put New Zealand top of their Group C with three wins.
Such was their dominance of the group, which also featured Indonesia and Ireland, they lost only one wicket in the tournament so far and used only three batswomen.
New Zealand advanced as top qualifiers in the Super 6 stage.
Points carry through from the group stage, with New Zealand top of Group 2 on net run rate from England.
Their next game is against Rwanda tomorrow night, followed by Pakistan on Wednesday morning.
The top two teams from each of the Super 6 groups advance to the semifinals.