Conway blasted 126 from 110 balls and Mitchell finished on 100 not out after New Zealand won the toss and elected to bat, making 318 for six.
Bangladesh were never in the hunt for the 319 target, all out for 154 after 42.4 overs, with Mahmudullah’s unbeaten 76 the only highlight as eight batsmen failed to reach double figures.
Jimmy Neesham and Matt Henry did the damage for New Zealand with the ball, taking five for 27 and four for 27 respectively.
With his maiden international hundred (126 from 110) Devon Conway is the @ANZ_NZ Player of the Match at the… https://t.co/znFQP4SUA7
— BLACKCAPS (@BLACKCAPS) 1616737190000
Paceman Rubel Hossain was the pick of the Bangladesh bowlers, with three for 70, but the tourists’ attack struggled on a green Basin Reserve wicket.
“We were just not good enough,” Bangladesh skipper Tamim Iqbal said.
“No doubt the Black Caps played unbelievably well but we didn’t perform. Sometimes the small things can hurt you, the (dropped) catches and the run-out chances.”
Conway capitalised on the tourists’ woes and his century was just reward for the South Africa-born batsman, who has been in outstanding form since he was first selected for the Blacks Caps late last year.
His performances include 72 in the second Bangladesh ODI and an unbeaten 99 when he was left stranded in a Twenty20 match against Australia last month.
Mitchell looked like he would suffer a similar fate in Wellington before scrambling home to bring up his century on the last ball of the innings as wicketkeeper Mushfiqur Rahim tried to stump him.
“I was just trying to swing as hard as I could, there were a few played and missed in there,” Mitchell said.
“I’ll take them any way they come. It’s just nice to get the job done.”
Both Conway and Mitchell were making only their third ODI appearances for New Zealand after debuting in the series opener against Bangladesh in Dunedin last week.
New Zealand were looking shaky before their arrival after losing three wickets within 13 balls to slump to 57 for three.
Tom Latham and Conway consolidated with a 63-run partnership before the New Zealand skipper departed for 18.
That was the cue for Conway and Mitchell to go on the attack, combining for a 159-run stand that put the match beyond Bangladesh’s reach.
Openers Tamim Iqbal and Soumya Sarkar were dismissed in the first five overs and a steady stream of wickets prevented any meaningful partnerships forming.
The teams will met next in a three-match Twenty20 series opening in Hamilton on Sunday.