Dropped on five and 10 off paceman Doug Bracewell behind the wickets, the flamboyant Tamim punished the visitors with 17 boundaries during his 153-ball knock.
The 24-year-old left-hander, who was first dropped by wicketkeeper BJ Watling and then by captain Brendon McCullum, maintained a brisk scoring rate during a 67-run stand with Marshall Ayub (41) for the second wicket and a third-wicket partnership of 76 with Mominul Haque (47).
Kane Williamson leapt in the air to snare a catch to dismiss Tamim, who has not scored a test hundred since June 2010, as the batsman tried to guide Wagner through the gully region.
All-rounder Shakib Al Hasan (20) fell leg before wicket to young leg-spinner Sodhi at the stroke of tea.
A heavy downpour during the break ensured that no further play was possible for the rest of the day.
The first match of the two-test series ended in a draw.
(Writing by Sudipto Ganguly; editing by Patrick Johnston)
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