When the Black Caps declared, pace bowlers Boult and Tim Southee then showed how to move the ball on a verdant surface as they ripped through the Bangladesh line-up.
Boult ended with five for 43 while Southee took three for 28.
Only two relative Test novices, Yasir Ali and Nurul Hasan, provided any resistance.
Yasir, in his third Test, made 55 while Nurul was out for 41 in his fifth Test.
The tourists lost their first four wickets for only 11 runs inside seven overs and were then five for 27 before Yasir and Nurul mounted a 60-run salvage mission.
In the blitz start, Boult had Shadman Islam (seven) and Najmul Hossain Shanto (four) both caught by Latham at second slip while Southee bowled debutant Mohammad Naim and captain Mominul Haque without scoring.
The fifth wicket fell in the first over after tea when Boult had Liton Das caught behind for eight.
Southee came back to break up the Yasir-Nurul partnership with a ball that came back sharply on Nurul and he was trapped lbw.
Boult bowled Mehidy Hasan (five) to become the fourth New Zealander -- behind Richard Hadlee, Daniel Vettori and Southee -- to take 300 Test wickets.
Kyle Jamieson removed Taskin Ahmed (two) and Yasir before Boult finished off the innings bowling Shoriful Islam for two.
Latham's two catches in slips came after his marathon innings, the second double century of his career.
He faced 373 deliveries and hit 34 fours and two sixes with the innings coming to an end when he tried to up the run rate.
He smacked a six, four and another six off successive Mominul Haque deliveries but mistimed his fourth attempt to hit the Bangladesh captain and part-time spinner to the boundary and was caught at square leg.
Conway, resuming on 99, brought up his hundred with a four off the first ball of the day but was run out soon after.
It ended a 215-run second-wicket partnership following Latham's 148-run stand with Will Young for the first wicket.
New Zealand's elder statesman Ross Taylor, playing his 112th and final Test, received a guard of honour on his way to the middle from the Bangladesh players and was quickly into his trademark strokes, with boundaries from a cover drive and a cut shot.
But on 28 he was caught by Shoriful Islam at square-leg off Ebadot Hossain and Henry Nicholls (duck) and Daryl Mitchell (three) followed soon after.
Blundell was unbeaten on 57 with Jamieson on four when the declaration was made.