Openers Peter Fulton and Hamish Rutherford laid the foundation with a 57-run stand after the tourists elected to bat on the newly-laid wicket at the Zahur Ahmed Chowdhury stadium.
The pair defied the Bangladesh bowlers on the slow, low pitch for 23 overs before Rutherford top-edged spinner Sohag Gazi to mid-off after scoring a fluent 34.
Rutherford hit three boundaries and a six.
Fulton was unbeaten at lunch on 38 and Kane Williamson was on 15, the pair having added 36 runs so far for the second wicket.
Bangladesh, who went in with three spinners -- Abdur Razzak, Gazi and Shakib -- brought on the slow bowlers in the sixth over itself to take advantage of the low bounce.
The Black Caps awarded Test caps to leg-spinner Ish Sodhi and all-rounder Corey Anderson, while batsman Marshall Ayub was making his debut for the hosts.