Najmul, Mominul lead Bangladesh fightback against New Zealand
Skipper Najmul was on 48 and Mominul on 38 at the break to help the hosts recover from 26-2.
New Zealand made 317 in their first innings to take a slender seven-run lead.
Ajaz Patel trapped opener Zakir Hasan leg-before for 17 and Tim Southee directed a straight drive by Najmul onto the stumps at the non-striking end to run out Mahmudul Hasan for eight.
Mominul, who joined Najmul in the rescue act, was also the hero for Bangladesh with the ball, having taken the last two New Zealand wickets in the morning.
The tourists, replying to Bangladesh's first-innings 310, resumed on 266-8, still 44 runs behind.
Southee and Kyle Jamieson frustrated Bangladesh for more than an hour to share 52 runs for the ninth wicket, until left-arm spinner Mominul removed them both in the same over.
Mominul trapped Jamieson leg-before for 23 to leave New Zealand 316-9, and then bowled Southee four balls later for 35 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.