Young and Nicholls combined for a 97-run partnership for the third wicket, highest for New Zealand in this stand at Mirpur venue, after being slumped to 16-2.
New Zealand made a watchful start but left-arm pacer Mustafizur Rahman broke through, by sending back opener Finn Allen for 9.
In his next over, Mustafizur had Chad Bowes caught by Nurul Hasan after he edged behind for 1.
Young and Nicholls survived some excellent bowling of Mustafizur and Tanzim Hasan and kept the side unscathed in a bowling favorable condition.
They also dealt the Bangladeshi spinners confidently before Mustafizur came back in his second spell to trap Nicholls leg-before.
Young, who hit four fours and one six in his 91-ball innings, threw his wicket after trying to charge left-arm spinner Nasum Ahmed needlessly.
Nasum also handed Rachin Ravindra a second-ball duck before the rain had the final say.
- AP