The South African-born wicket-keeper compiled a career-best 103 as the Black Caps recovered from 282 for seven to post 469 all out by tea on the second day at the Zahur Ahmed Chowdhury stadium. Kane Williamson had top-scored with 114.
Bangladesh were 103 for two in reply at close, following a breathtaking counter-attack by 22-year-old Mominul Haque, who smashed an unbeaten 77 off 71 balls with 13 boundaries.
Mominul shared an unbroken third-wicket stand of 95 with debutant Marshall Ayub (21 not out) after two wickets had fallen for eight runs by the fourth over.
New Zealand 469 (Peter Fulton 73, Kane Williamson 114, BJ Watling 103; Abdur Razzak 3 for 147) lead Bangladesh 103 for 2 (Marshall Ayub 21*, Mominul Haque 77*; Trent Boult 1 for 5) by 366 runs.