Tim Southee and Kyle Jamieson shared a 52-run stand for the ninth wicket to give New Zealand a seven-run first-innings lead in the first Test in Sylhet on Thursday.
After New Zealand were all out for 317 on the third morning, in reply to Bangladesh's 310, the hosts negotiated a tricky nine overs before lunch to reach the break on 19-0.
Zakir Hasan was on 14 alongside Mahmudul Hasan, the first innings top scorer with 86, who was five not out.
New Zealand took the honours in the opening session of the day thanks to their captain Southee, who was last man out for 35, and Jamieson who made 23.
New Zealand resumed on 266-8, still trailing by 44, with Bangladesh looking to wrap up the innings quickly.
But the tail-end pair frustrated Bangladesh for more than an hour until part-time left-arm spinner Mominul Haque removed them both in the same over.
Mominul trapped Jamieson leg-before to leave New Zealand 316-9 and then bowled Southee four balls later to finish with career-best figures of 3-4.
Southee hit three boundaries in his 62-ball stay.
The two-match series is the beginning of a new cycle in the World Test Championship for both teams.
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