England started day 3 on 50 for 2, but Tim Southee got the wicket of overnight batsman Nick Compton for 13 in the third over of the day.
Southee soon removed Ian Bell for 17 to leave England reeling.
Trent Boult had another great day, finishing with figures of 6 for 68 as England were bowled out for 204 conceding a 239-run first-innings lead.
Joe Root was the last man to go. He made 45 but got no support from the English tail-enders.
Matt Prior was quite fluent during his innings of 73 hitting 13 boundaries. (Getty Images)
Stuart Broad made early inroads to put New Zealand in a big spot of bother. New Zealand closed the day on 33 for 2, taking their lead to 274. (AP Photo)