How, whose previous highest Test score was 37, was dismissed for 92 in the final session at Seddon Park when he was well caught by Paul Collingwood off Monty Panesar before New Zealand ended the day on 282 for six.
Ross Taylor will resume on Thursday on 54 with captain Daniel Vettori on four. Wicketkeeper Brendon McCullum had produced a dashing 51 off 55 balls before he was dismissed in the penultimate over of the day.
He and Taylor had combined for an 86-run partnership after New Zealand looked to have squandered their chance to build a big first innings when they lurched to 191 for five.
Pick of the attack
All five of the England bowlers took a wicket with Sidebottom the pick of the attack with two for 39 off 21 overs.
Despite How's composed innings and the partnership between Taylor and McCullum, New Zealand should have capitalised more on the benign pitch in ideal batting conditions after Vettori had won the toss and chosen to bat.
New Zealand's run accumulation was stymied by brilliant catches from the England fielders just as they were beginning to build partnerships. Alastair Cook produced two spectacular catches at gully, with his one-handed diving effort at full stretch to dismiss Stephen Fleming for 41 off Sidebottom after lunch the highlight of the display.
He produced a similar effort to catch the dangerous Jacob Oram for 10 during the final session, while he also took a sharp chance to dismiss Matthew Bell for 19 in the first session.
SCOREBOARD
NEW ZEALAND (I Innings)
How c Collingwood b Panesar 92
Bell c Cook b Harmison 19
Fleming c Cook b Sidebottom 41
Sinclair c and b Collingwood 8
Taylor (batting) 54
Oram c Cook b Hoggard 10
Mc’llum c Ambrose b S’bottom 51
Vettori (batting) 4
Extras (LB-2, NB-1) 3
Total (for 6 wkts; 90 overs) 282
Fall of wickets: 1-44, 2-108, 3-129, 4-176, 5-191, 6-277
Bowling: Sidebottom 21-8-39-2, Hoggard 21-1-95-1, Harmison 15-2-64-1, Panesar 26-7-66-1, Collingwood 7-2-16-1.