It was a smart piece of bowling from Wagner and wise captaincy from Brendon McCullum as they played on the aggressive nature of Iqbal who got overexcited.
Shortly after, leg-spinner Ish Sodhi then trapped Shakib Al Hasan lbw for 20, as New Zealand began to grab the upper hand in the contest as the tea interval was called for.
Bangladesh skipper Mushfiqur Rahim was at the crease when Al Hasan was dismissed and he will be joined by Nasir Hossain when play resumes on day two.
Earlier on day one, Rahim won the toss and chose to bat on another slow sub-continent wicket and New Zealand gifted Iqbal with two extra lives.
The hard-hitting left-hander was dropped on five by Watling and 10 by McCullum - both from the bowling of Doug Bracewell - as he chased wide deliveries.
Bangladesh did lose opener Anamul Haque early on for seven as he tried to pull a Trent Boult delivery that wasn't there to do so, which brought No 3 Marshall Ayub to the crease.
Ayub (41) and Iqbal added 67 for the second wicket before Ayub became the first of Wagner's victims for the day.
From there, Iqbal boxed on before New Zealand's bowlers brought the visitors back in to the match but they were too inconsistent for large parts of the day.
Wagner, who was brought in to the New Zealand side in place of spinner Bruce Martin, finished the day with 2-42 and was the pick of the bowlers.
Boult, Sodhi and Anderson each finished the rain-shortened day with one wicket.
Bangladesh made one change to their side from last week's test as seamer Al-Amin Hossain was picked for his test debut after Robiul Islam was ruled out through injury.
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