They are confident, playing well against a West Indian team with collective backs to the wall and can sense another win to wrap up what would be a highly impressive home series victory - a first since 2006, coincidentally against the same opposition.
For the captain, Brendon McCullum, there is a balancing act to perform.
He likes being positive, taking hunches, blessed with a gambler's perspective on the game. This time, there is also the imperative not to allow the West Indies to draw level at the last stop.
"It's a delicate balance," McCullum said yesterday.
"My mindset is very much about trying to attack, especially if you're uncertain. But there are times you have to play the long game. We've played really good cricket in the last two tests and want to continue the momentum we've built up.
"The feeling everyone experienced in the dressing room the other day [at the Basin Reserve after the innings and 73-run win] is something that people will hold on to as a motivating factor every time they rock up and play another test."
New Zealand have passed 400 in the first innings of their last four tests - exceeding 600 at University Oval early this month - and have found the advantages that can bring when you possess a quality seam attack.
Trent Boult and Tim Southee have been, along with rejuvenated batsman Ross Taylor, the New Zealand kingpins of the series.
They had an extra couple of days rest with the early finish in Wellington and McCullum has high praise for the Northern Districts' pair and their backups.
"Over the last 12 months those guys have been very consistent and turned in excellent performances," McCullum said. "Trent got the rewards in the last game and Tim got the rewards at Lord's [in May] but throughout the year, even in trying conditions, those guys continue to run in and present us with good opportunities."
As for the West Indies, it's time to pull out a big shovel. They would have been dead in the series but for Darren Bravo's courageous double century at Dunedin.
Their seam bowling hasn't been good enough, their batting not dedicated or resourceful enough.
This is not news to the tourists. Their coach Ottis Gibson has spelled out what is required. Captain Darren Sammy reiterated it yesterday.
"The coaches can coach, but the players have to play and try to give an extra 20 per cent - be hungry, be selfish, whatever it takes," he said.
"That's the only way we can beat New Zealand in these conditions. It will take a big effort from us but it's not something that's impossible."
The Seddon Park surface, under new curator Andy Brown, had good grass cover yesterday, but looks browner than either of the first two test strips. Good runs should be on offer through the middle of the match.
Seddon Park, from 10.30am today
New Zealand: Brendon McCullum (c), Hamish Rutherford, Peter Fulton, Kane Williamson, Ross Taylor, Corey Anderson, BJ Watling, Tim Southee, Ish Sodhi, Neil Wagner, Trent Boult.
West Indies: (from) Darren Sammy (c), Kieran Powell, Kirk Edwards, Kraigg Brathwaite, Darren Bravo, Marlon Samuels, Shiv Chanderpaul, Narsingh Deonarine, Denesh Ramdin, Tino Best, Shannon Gabriel, Sheldon Cottrell, Sunil Narine.
