The Blackcaps will enter day five looking to avoid a first defeat to Bangladesh in test cricket, ahead by just 17 runs with five second innings wickets in hand.
Bangladesh, who are yet to win in any format against the Blackcaps on Kiwi soil, will begin the final day chasing a victory against the World Test Champions as New Zealand will hope more than anything to save face, as much as save the first test.
Beginning the fourth day the Blackcaps finally managed to dismiss the visitors for 458 - 130 runs ahead after their first innings - before Bangladesh reduced New Zealand to 147/5 at the end of play.
A stunning spell from Ebadot Hossain (4/39) triggered a middle order collapse as the Blackcaps lost three wickets without scoring a run to have Bangladesh dreaming of victory on day five.
New Zealand's overnight pair of Ross Taylor (37 not out) and Rachin Ravindra (six not out) will resume their innings on Wednesday as the Blackcaps seek to avoid a first home test defeat against any nation since 2017.
Returning at 401/6, Bangladesh's overnight pair of Yasir Ali (26) and Mehidy Hasan Miraz (47) pushed their partnership to 75 runs for the seventh wicket as the visitors' lead swelled into triple figures.
But after drinks in the morning session Tim Southee struck for his first wicket of the test as Mehidy was out caught behind by Tom Blundell shy of his half-century, while Kyle Jamieson took his first wicket to remove Yasir - strangled down the leg-side.
Southee struck again to remove Taskin Ahmed lbw for five before Trent Boult claimed the final wicket of the innings, clean bowling Shoriful Islam for seven to bowl Bangladesh out for 458 - 130 runs ahead in the first innings.
Boult finished as the pick of the bowlers with 4/85 as the New Zealand opening pair of Tom Latham and Will Young navigated a tricky passage of play to get through to lunch at 10/0.
After lunch however, New Zealand were immediately on the back foot as Latham fell, dragging Taskin Ahmed back onto his stumps for 14.
Fresh from his 122 in the first innings Devon Conway crawled to 13 before he became the second Blackcap to fall.
As part of a huge nine-over spell from Ebadot Hossain before tea Conway was out caught after inside edging onto his pad as the ball fell to Shadman Islam coming forward behind the wicket.
Losing two wickets in the afternoon session the Blackcaps reached tea at 68/2, still 62 runs away from making Bangladesh bat again.
But undeterred by the loss of his partners, Young batted on joined by Ross Taylor and reached 50 for the second time in the match, coming from 134 balls with five boundaries.
At the other end Taylor was dropped on 17 - slog sweeping straight to Shadman Islam on the midwicket boundary - as he and Young added a half-century stand for the third wicket.
The pair combined for 73 runs together and saw New Zealand take the lead until Young became the third Blackcap to fall. A length ball from Ebadot Hossain kept a touch low as Young's attempted pull shot was beaten and lost his off-stump to walk off for 69.
Two balls later Ebadot had Henry Nicholls clean bowled for a second ball duck and then removed Blundell for a fourth ball duck. From 136/2, the Blackcaps had lost three wickets without scoring to be 136/5.
Taylor and Ravindra survived until the end of play but will return to the crease with a monumental task on their hands to avoid a history-making loss.
Bangladesh meanwhile are all but certain to avoid their run of nine consecutive test defeat on Kiwi soil and will return to Bay Oval as the bookies' favourites to complete one of cricket's most remarkable victories.
Join Newshub for live updates of the Blackcaps v Bangladesh from 11am Wednesday.