The 29-year-old old also combined with Tom Bruce (59 not out) in a 123-run partnership in 11.1 overs to threaten a total in excess of 200 before Bangladesh's bowlers pulled the run rate back towards the end of the innings.
The visitors were well placed at 104-3 in the 11th over of their reply but once Soumya Sarkar (39) and Sabbir Rahman (48) were dismissed, the momentum was sucked out of their run chase and they were bowled out for 148 in 18.1 overs.
New Zealand, who already had Guptill (hamstring) and Neil Broom (broken finger) out injured, also lost wicketkeeper Luke Ronchi to a groin strain when he pulled up chasing a ball in the eighth over, leaving Bruce to take over behind the stumps.
Ronchi was later ruled out of the final game of the series on Sunday with uncapped Wellington wicketkeeper Tom Blundell replacing him in the squad.
Munro raced to 50 from 31 balls but flicked the switch in the 13th over when he belted off-spinner Mahmudullah for 28 runs to move from 64 to 92.
He brought up his century when he pushed the ball back past Mashrafe Mortaza for a single on his 52nd delivery, having hit seven boundaries and seven sixes, but was dismissed shortly after when he nicked behind off Rubel Hossain.
Rubel finished with figures of 3-37 and was on a hat-trick at one stage, having bowled Colin De Grandhomme on the final delivery of his third over, the 17th, and Jimmy Neesham on the first ball of his fourth, the 20th.
(Reporting by Greg Stutchbury in Wellington and Amlan Chakraborty in New Delhi; Editing by John O'Brien)
