Latham dominated the crease for more than 47 overs as he faced 121 deliveries and smacked four sixes and seven fours.
Colin Munro chimed in with a rollicking 87 in a 158-run partnership with Latham for the fifth wicket to bolster the innings when the rest of the top order failed to stick around.
After winning the toss and electing to bat, New Zealand maintained a steady run rate without offering prolonged support to the left-hander Latham at the top of the order.
Martin Guptill was primed for a blistering start and smacked an early six but on 15 he misread a slower Mustafizur Rahman delivery and skied the ball to Soumya Sarkar at mid-off.
Captain Kane Williamson moved smartly to 31 before he was undone by Taskin Ahmed, while Neil Broom (22) and Jimmy Neesham (12) came and went in quick succession as New Zealand slumped to 158-4 in the 28th over.
But Latham, who had a heart-stopping moment on seven when Mushrafe Mortaza had a ball come back and sail just over off stump, soldiered on to surpass his previous best 110 not out against Zimbabwe last year.
He was eventually dismissed with 15 balls remaining in the innings when he edged a wide delivery from Mustafizur through to Mushfiqur Rahim behind the stumps.
The big-hitting Munro pounded four sixes and eight boundaries in his 61-ball stand.
Shakib al Hasan was the most successful of the Bangladesh bowlers with 3-69 while Mustafizur, in his first ODI in five months following shoulder surgery, took two wickets as did Taskin Ahmed.
PTI