Until the rearguard, Trent Boult (three for 52), Tim Southee (three for 48), Neil Wagner (three for 44) and Colin de Grandhomme (one for 27) worked in partnerships and bowled a variety of competitive lengths that exposed Bangladeshi hesitation. Spinner Mitchell Santner never took the ball in either innings.
The Black Caps knocked off the chase for 109 in 18.4 overs, taking advantage of an extra half hour's grace granted by the umpires.
The hosts showed their intent by promoting Colin de Grandhomme to No.3, after Jeet Raval was bowled by Kamrul Islam Rabbi for 33. De Grandhomme made 27 from 13 balls and hit the winning runs;
Tom Latham finished 41 not out at the other end.
In the course of the victory Southee became the fifth New Zealander and second-fastest to 200 test wickets.
He enticed Shakib Al Hasan to guide a ball to de Grandhomme at deep gully to complete the feat in his 56th test, behind Sir Richard Hadlee (44), but in front of Chris Cairns (58), Chris Martin (62) and Daniel Vettori (63).
New Zealand's innings ended in bizarre circumstances, when Wagner was run out for 26. He got his bat behind the line and leapt into another stride, as wicketkeeper Nurul Hasan back-handed a ball to dislodge the bails.
He was dismissed, as per law 29, because neither foot had yet been grounded behind the popping crease. It can't be long before that law is rescinded.
Wagner formed a 57-run ninth-wicket partnership with Henry Nicholls, who fell two short of his maiden test century, after dragging an edge onto the stumps trying to drive off-spinner Mehedi Hasan Miraz.
He snicked through a gap in the slip cordon to reach 90, a French cut took him to 97 and a miscued hook off a glove landed innocuously, as he moved to 98 in front of his home crowd.
Nicholls faced pressure and responsibility, moving to his highest test score in his 17th innings. His average rose from 26.57 to 31.33, the first time it has breached 30 since his debut against Australia last summer.
Resuming on 56, he answered questions about his role at No.5 and has presumably cemented his position for the South African series.
Catching remained a problem throughout the test, as it did at Wellington, with 12 chances (Bangladesh seven, New Zealand five) dropped.
Taskin Ahmed, with pace in the 140km/h bracket, was the pick of the Bangladeshi bowlers, despite relatively lean figures. He suffered the most from his team-mates' butterfingers.
The start of play was delayed by 30 minutes, courtesy of a leak in the pitch covering. It required an area just outside a left-hander's off stump at the Port Hills end to receive urgent "Sir Alex Ferguson" treatment with two industrial hair dryers.
