On Friday they will try to win their second series in 19 attempts at home.
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David Leggat: Take out the rain and fans couldn't ask for more from pink ball test
The achievement of the 1983-84 summer was by a New Zealand team in the ascendancy.
Martin and Jeff Crowe, Jeremy Coney and Ian Smith made their maiden test centuries; Sir Richard Hadlee was in his pomp as an all-rounder; and a wave of self-belief was building.
They dismissed an England side – which Britain's Mail on Sunday accused of smoking dope on tour - for 82 and 93 in Christchurch, to win by an innings and 132 runs.
The performance of the current New Zealand side to defeat England by an innings and 49 runs, a consecutive victory after the 2015 triumph in Leeds, suggests they have the capability to repeat.
"[I was impressed by] our grind," coach Mike Hesson said, reflecting on the Eden Park win.
"The wicket didn't offer a lot and the ball got soft, but we hung in there and stayed disciplined. We knew we'd have to invest the whole day. Thankfully we gave ourselves 20 overs' grace."
Hesson differentiated between "first and second innings bowlers" after man-of-the-match Trent Boult and Tim Southee took 10 wickets as the only bowlers used in the opening session.
"You can't pick a side with guys who only perform on day one. Neil Wagner [three for 77 from 32 overs] is testament to that and Todd Astle [three for 39 from 16.1 overs] did a great job too.
"When there's not a lot happening, Neil makes things happen. The balance of the attack allows him to play that role in the second innings."
Astle was a debated pick after Mitchell Santner's knee injury, given the perception fellow leg spinner Ish Sodhi attacks more.
Hesson defended the selection.
"A lot of the debate comes from people who don't watch first-class cricket. Todd has been amazing there for three or four years and is a fine bowler.
"He just hasn't earned the opportunities because the likes of Dan Vettori and Mitchell have been in that role.
"He has good variation and brings the stumps into play, which is what you need on day four and beyond. He doesn't get the bounce of some other guys, but brings lbw and bowled into play, which is what we needed yesterday."
Hesson expected the red ball in Christchurch to offer challenges deeper into the innings.
"The pink ball swung for eight to 10 overs, but if you could withstand that you got some respite. The red ball probably won't allow that, so different preparation is required."
England captain Joe Root denied his side had a skill level problem after suffering their fifth innings defeat in eight away tests.
"We didn't adapt quickly enough to the conditions [early in the test].
"It's disappointing because we're used to balls swinging and seaming around. At no stage [in the first innings of 58] did anyone get themselves in and create the partnerships fundamental to get scores of 350-400 plus and build scoreboard pressure."
