After finishing 485 all-out, England reduced NZ to 66-3 at close of play.
England resumed day two on 267-2 but top-scorer Jonathan Trott failed to add to his overnight score of 121, before being dismissed by Trent Boult.
His partner at the crease, Kevin Pietersen, batted his way to 73 however and Matt Prior led a lower order attack with 82 from 99 balls.
Prior’s eighth wicket partnership of 83 with Steven Finn helped England score way over 400, ensuring the tourists did not waste the good work from day one.
Kiwi bowler Bruce Martin finished with figures of 4-130 from the innings, whilst Kane Williamson took the final two English wickets in the same over for his total of 2-16.
With New Zealand trailing the visitors by some margin they needed to bat strongly in their first innings.
But James Anderson peppered the opening batsmen in his spell with the ball and Black Caps’ Peter Fulton could only score one off 24 balls, before edging to Alastair Cook off the Lancashire man’s bowling.
Hamish Rutherford and Williamson began to steady the ship for the hosts, before two wickets in two balls from Stuart Broad swung the tie back in England’s favour.
First Rutherford edged the ball to the slips, again caught by Cook and then Ross Taylor was clean bowled by Broad the very next ball.
At 48-3 things began to look perilous for New Zealand as the follow-on target of 266 still seemed a long way off.
Williamson and new batsman Dean Brownlie got their side to 66 before stumps on day two, but they still trail England by 399 runs and have to face an in-form Broad and Anderson when day three resumes at 9.30pm GMT.