Bangladesh No 4 Mominul Haque came out and played like he had a bus to catch as he rattled through to 77 not out and brought up his 50 from only 36 balls.
Debutant leg-spinner Ish Sodhi wasn't given long to spectate proceedings when he was tossed the ball by New Zealand skipper Brendon McCullum in the 10th over of the innings.
Sodhi and fellow tweaker Bruce Martin were loose early on, despite the dusty wicket at the Zahur Ahmed Chowdhury Stadium being ideal for spin bowling.
Sodhi warmed to his work though as he finished the day with the economical figures of 0-27 from eight overs but Martin was pulled early after his three overs disappeared for 20.
New Zealand skipper Brendon McCullum rotated his bowlers in short spells but Haque was relentless in his pursuit of runs and didn't spare anybody as he blazed away.
The 22-year-old found a willing partner in debutant Marshall Ayub, who took a disciplined approach to his innings as he didn't strike a boundary until his 63rd delivery, which was a stark contrast to Haque.
Bangladesh closed the day on 103-2 with Haque and Ayub (21 not out) at the crease but still face a long day in the middle tomorrow (fri) if they want to avoid the follow-on as they try to assert themselves in the match.
Earlier, New Zealand begun day two on 280-5, but lost Martin and Corey Anderson for very little and the visitors were looking at being bowled out short of 300 when they were 282-7.
No 9 Bracewell then combined with wicketkeeper BJ Watling to add a valuable 57 for the eighth wicket, which began the salvage mission for the Black Caps.
Bracewell eventually went for a patient 29 before Sodhi joined Martin and Anderson with a solitary run next to his name before he was dismissed.
At 342-9, Bangladesh may have been happy with their work but Watling and Boult systematically destroyed any good feelings the home side would have had about their bowling effort.
The unlikely pair added 127 for the final wicket - the equal ninth-highest partnership for the 10th wicket in test cricket - as Boult became only the 15th player to score a half century from No 11 as he finished unbeaten on 52.
Watling was the last man out when he was stumped for 103 - his second test ton and his highest score in the whites - but the damage was done by then.
New Zealand will look to turn the screws on day three on the low-and-slow wicket.
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