B-J Watling bottom-edged onto the stumps in Shakib's next over and Colin de Grandhomme drove around a delivery three balls later.
The solid platform, built via a 106-run third wicket stand between Ross Taylor (77) and Tom Latham (68), was teetering.
Taylor's quest to equal his late mentor Martin Crowe's New Zealand record of 17 test centuries ended 15 minutes before tea.
He hit a catch, which had its merits debated for bump ball, to substitute fielder Taijul Islam at short mid-wicket from off spinner Mehedi Hasan. Third umpire Marais Erasmus ruled in the tourists' favour.
The majority of Taylor's runs came from slashes and caresses between cover and backward point. He muscled one pull for six, but refrained from driving between extra cover and mid-on. A stroke through point for three from Mehedi took him to 62... and 6000 test runs. He is the third New Zealander and fastest (145 innings) to the mark, compared to Brendon McCullum (163) and Stephen Fleming (165).
Bangladesh pace bowler Kamrul Islam dropped the No.4 when he dropkicked Mehedi to deep square leg on 75. The innings was further evidence surgery to remove the pterygium on his left eye in late November was a success.
He has since had domestic T20 scores of 82 not out and 80, and test scores of 40, 60 and 77.
Kamrul delivered momentum for Bangladesh in the morning session.
He lured Jeet Raval into playing-on via a miscued pull shot in the 15th over for 16. Two balls and two runs later captain Kane Williamson edged an outswinger behind, presenting debutant wicketkeeper Nurul Hasan with his maiden test dismissal. Nurul headed to the legside before recalibrating with the ball's movement. The ground descended into silence beyond the boundary rope as the New Zealand captain traipsed off at 47 for two; conversely the field of play was a carnival of rejoicing Bangladeshis, led by an ecstatic Kamrul. He finished with two for 48 from 13 overs.
Rubel Hossain's aggression complemented the attack, despite suffering a bang to the helmet and knock to the elbow from Trent Boult on the opening day. A bandage protected the elbow, but nothing shielded his vocal chords as he bellowed after most deliveries.
The bowlers' efforts were literally let down by the fielders. Three catches were dropped and one opportunity was missed.
In the fourth over Mahmudullah spilt Raval on two off Mehedi; that was followed by an edge which went begging in the 11th over to second slip Sabbir off Taskin Ahmed; Kamrul dropped Taylor; and Nicholls, on two, flashed a ball at silly point Nazmul Hossain off Mehedi. The ball stuck in Nazmul's arms as he took evasive action... before trickling onto the turf.