Left-arm paceman Boult then removed Bangladesh opener Tamim Iqbal for a duck with his second ball, before a 36-ball half century to 22-year-old Mominul Haque (77 not out) took his side through to 103 for two at the close.
The hosts had visions of bowling New Zealand out before lunch when Bruce Martin (1) and debutant Corey Anderson (1) were out within the first two overs of the day. Doug Bracewell (29) then combined with Watling in an eighth wicket stand of 57.
After Bracewell fell to Sohag Gazi debutant legspinner Ish Sodhi (1) quickly followed.
Watling played a typically gritty innings when he was reprieved after scoring four. Television replays showed paceman Rubel Hossain had overstepped when Watling was caught in the gully.
The late rally appeared to rattle Bangladesh, with Anamul Haque (3) following Tamin Iqbal back to the pavilion early in Bangladesh's first innings, lbw to Bracewell.
(Reporting by Josh Reich; Editing by John Mehaffey)
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