Tracey Neville's side booked their place in the semi-finals of the competition as group winners, with New Zealand now facing an anxious wait to see whether they will also reach the last four.
A low-scoring encounter saw both sides match each other throughout the first quarter, scoring 12 points apiece, and the second quarter was similarly close.
England went into half time with a 26-24 advantage, but that grew further in the third as England took it 14-10 to edge closer towards top spot.
New Zealand went into the match needing victory to guarantee their place in the semi-finals following their shock defeat to Malawi earlier in the group stages, but they struggled to ever get on top throughout the match.
England also took the final quarter 14-11 to seal their nine-point victory, confirming their place in the Saturday's semi-final.