Latham raised 148 runs with fellow opener Will Young and then consolidated New Zealand's position with his still-flourishing 201-run stand with Devon Conway, who remained not out on 99.
"The way Tom hit some of his drives, the sound of ball meeting the bat was awesome," New Zealand batting coach Luke Ronchi told reporters.
"To be not out and bat the whole day and to be continuing tomorrow with Devon...it was a fantastic effort from both ends."
Smarting from their shock defeat in the series opener, world Test champions New Zealand got the perfect start with Latham leading by example after being put into bat at Christchurch's Hagley Oval.
The left-hander, leading the side in absence of an injured Kane Williamson, was given out lbw to Ebadot Hossain twice in the ninth over and both decisions were reversed after the batsman reviewed them.
Ebadot created another chance soon after the lunch break but Liton Das spilled Young, then on 26, at second slip with the batsman rubbing salt in the wound with a rare seven runs after running three and picking up four overthrows.
Shoriful Islam finally broke the stand when he had Young caught at gully for 54 but Latham continued to punish the wayward Bangladesh bowlers as he raced to a 133-ball century.
Latham, whose free-flowing knock included 28 boundaries, was on 169 when Bangladesh blew a review trying to get him caught behind.
"Unfortunately we did not bowl enough good balls to create the sort of pressure that we created last week," Bangladesh fast bowling coach Ottis Gibson told reporters.
"New Zealand would have been hurting from last week and they came back and showed why there are one of the best teams in the world."
Bangladesh were forced into making two changes to the squad that had triumphed in Mount Maunganui.
Opener Mahmudul Hasan (hand) and middle order batsman Mushfiqur Rahim (groin) missed out with injuries and were replaced by Nurul Hasan and Mohammad Naim.
New Zealand brought in Daryl Mitchell for fellow all-rounder Rachin Ravindra