"Funny things can happen on the last day, as it did against Pakistan in the last series," record-setting opener Tom Latham said, referring to the nine-wicket tumble in the final session in Hamilton in late November.
"It's a massive job for us to do in the morning. If we can get three quick wickets then you never know."
Bangladesh fast bowler Taskin Ahmed is backing his batsmen though.
"If batsmen get set it's easy to score" the debutant said. "Still, batsmen have to bat well and have to be careful."
Run making has been pretty straightforward for much of the test and although there might be some fifth day variables in the bounce, the pitch won't break up any time soon.
Latham and Neil Wagner took contrasting, starring roles today.
Latham's 177 is the highest score by a New Zealand opener in 59 tests at the Basin, second only to South African Jackie McGlew's 255 not out in 1953.
Wagner then wore three short-pitched fliers on his helmet in the space of 15 balls from slippery Kamrul Islam, and was heard to mutter grudgingly that if you dish it out, as he frequently does, you have to cop it.
New Zealand's batting was built on partnerships.
Five stands went past 50; only Tim Southee failed to reach double figures, and Mitchell Santner, also struck on the helmet by Taskin, not only made his highest test score but snared a late wicket, then ran out nightwatchman Mehedi Hasan from a madcap final ball of the day with a direct hit from deep mid on.
New Zealand's idea was to get as close as possible to Bangladesh, then look to put a squeeze on. Declare behind to have more bowling time, but spotting the visitors a bigger lead? Not in the thinking.
"Possibly," Latham replied when asked if he sensed Bangladesh might be jittery.
"They've been ahead a lot in this match. If we can get into that middle and lower tail, there's still a lot of overs (98) left in the day and anything can happen."
Things started well enough for Bangladesh late in the day, before Imrul - who'd nabbed a world record for five catches as a replacement wicketkeeper - injured his thigh diving for his crease.
That was in the 13th over, and things unravelled rapidly from there. Tamim Iqbal was bowled by Santner five balls later, Mahmullah touched a legside catch of a fired-up Wagner before Mehedi's moment of madness.
Strange old game, this cricket.