Chasing a series-levelling victory, New Zealand appeared to nose ahead in the contest after bundling out Bangladesh for 172 at Mirpur's Shere Bangla Stadium.
The tourists had to contend with a top-order meltdown of their own when they came out to bat and they were reeling at 55-5 when bad light stopped play with only 79 overs bowled in the day.
Daryl Mitchell (12) and Glenn Phillips (five) will resume New Zealand's battle to stay in the contest when play resumes on Thursday.
Earlier opting to bat, Bangladesh slumped to 47-4 in 15 overs with New Zealand's spin duo of Mitchell Santner (3-65) and Ajaj Patel (2-54) wrecking their top order.
Mushfiqur (35) and Shahadat Hossain (31) combined in a 57-run stand to steady the ship until the 41st over when New Zealand prised out a wicket in the unlikeliest of fashions.
Mushfiqur defended a Kyle Jamieson delivery and then instinctively extended his right hand to push the ball away even though there was no chance of it hitting the stumps.
The TV umpire upheld New Zealand's appeal for what was previously known as handling-the-ball but was brought under obstructing-the-field dismissal in 2017.
Mushfiqur is the first Bangladesh batter to be given out obstructing the field, seven batsmen had previously been given out 'handling the ball' in test cricket.
Phillips wrecked Bangladesh's lower order with figures of 3-31.
New Zealand's top order could not master the spin-friendly conditions and looked ill at ease against Mehidy Hasan Miraz (3-17) and Taijul Islam (2-29).
Bangladesh won the opening test in Sylhet by 150 runs, their first on home soil against New Zealand.
