The hosts started the day on 337 for seven and added a disappointing 17 runs as Trent Boult and Tim Southee wrapped the innings up for 354.
Boult finished with impressive figures of five for 57 after adding the scalps of Steven Finn and James Anderson this morning.
But it was Matt Prior who was the key wicket, falling to Southee in the second over of the day after adding just a single to his starting score of 38.
England had been looking for a continuation of the vibrant eighth-wicket partnership between Prior and Graeme Swann that yielded 51 runs in just 59 deliveries at the end of last night's play.
Prior led that attack, with seven boundaries before the close, but managed just one run before succumbing to the 10th ball of the day.
Southee pitched it up and located an edge which Ross Taylor held well at first slip. It was a fitting result for Southee, whose patience and skill yesterday went largely unrewarded.
Finn was quick to follow Prior to the pavilion, comprehensively bowled by Boult immediately after bringing up the 350 with a crunching drive down the ground.
Swann was left stranded on 26 as Anderson became last man out, Boult completing a fine caught-and-bowled low to his right.