New Zealand spinners Mitchell Santner and Ajaz Patel took two wickets each to reduce Bangladesh to 80-4 at lunch on the first day of the second and final Test in Dhaka on Wednesday.
Mushfiqur Rahim (18) and Shahadat Hossain (14) were at the crease at Sher-e-Bangla National Stadium as the hosts attempted to rebuild from a poor start.
Bangladesh, who are chasing a first-ever Test series win over the Black Caps and lead 1-0, won the toss and elected to bat.
Zakir Hasan and Mahmudul Hasan put on 29 runs in the opening stand before Bangladesh lost four wickets for 18 runs to be reduced to a dismal 47-4.
Santner, who came into the side for Ish Sodhi in the tourists' only change, made the breakthrough when Zakir lofted a catch to Kane Williamson at mid-on after making eight runs.
Patel forced Mahmudul to give a catch to Tom Latham at short leg for 14 in the next over.
Tom Blundell then took a sharp catch behind the stumps as Mominul Haque (five) got an inside edge off Patel's next over.
Santner then trapped in-form skipper Najmul Hossain Shanto leg-before for nine.
Najmul was initially declared not out by the on-field umpire before the decision was reversed on review.
Bangladesh were unchanged from their 150-run victory in Sylhet in the first Test.