Nurul was 31 and Nazmul 15 with their 46-run partnership reviving Bangladesh from 179-5 to be 225-5 by tea at Hagley Oval in Christchurch.
They put the brakes on a New Zealand breakthrough when three wickets fell for 14 runs in a 16-ball burst after lunch including makeshift opener Soumya Sarkar for 86 and Shakib Al Hasan 59.
New Zealand had put the injury depleted Bangladesh unit into bat on the greenish wicket and had them 38-2 before Soumya and Shakib put on 127 for the third wicket.
In their place were Soumya for his fourth Test and a high score of 37 in his last outing two years ago, as well as the untested Nazmul and Nurul.
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Soumya, whose previous experience was batting at either six or seven, was up for the challenge.
His partnership with first Test double centurion Shakib raced along at nearly five an over, punishing anything short or wide to get Bangladesh out of early trouble.
But with Soumya's departure driving Trent Boult uppishly to a diving Colin de Grandhomme at cover, the door opened for New Zealand to get back into the match.
Bangladesh were lucky not to lose a fourth wicket when Nurul was dropped on two by Southee at second slip.
He offered another chance on 25 which flew between first and second slip leaving Ross Taylor and Jeet Raval staring at each other and neither moving.
It was the second mix up between the pair after a diving Raval had dropped Soumya on 52 when the ball was heading towards Taylor.