Bangladesh reached 104-2 at lunch on the opening day of the first Test in Sylhet after New Zealand spinners Ajaz Patel and Glenn Philips struck early on Tuesday.
Patel bowled opener Zakir Hasan for 12 and Philips dismissed Bangladesh captain Najmul Hossain Shanto for 37 for his maiden Test wicket.
At the break Mahmudul Hasan was batting on 42 alongside former captain Mominul Haque, who was three not out.
The hosts, who won the toss and elected to bat first, got off to a positive start with Mahmudul and Zakir putting on 39 runs.
Patel broke through with his left-arm spin as he bowled Zakir, a left-handed batsman, off a delivery that spun sharply.
Najmul, debuting as the 13th Test captain for Bangladesh, hit two fours and three sixes in his brisk knock before another attempted big hit off a full toss brought his downfall.
Kane Williamson ran back from mid-on to complete the catch, ending Najmul's 53-run second-wicket stand with Mahmudul.
The two-match series marks the beginning of a new cycle for the World Test Championship for both teams.
Shahadat Hossain made his debut for Bangladesh, while New Zealand selected Philips and Kyle Jamieson ahead of Rachin Ravindra and Neil Wagner.
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