For the first time in the series, it wasn't the batting which let the side down.
Taylor's unbeaten 107 off 93 balls led the way. At one point he clobbered 42 off 13 balls and completed his hundred with two balls left in the innings. He had a life at 12, when fast-medium Rubel Hossain dropped a caught and bowled chance.
But he got better, and more damaging, as his innings progressed.
Lefthander Munro, cheerily reverse sweeping his way towards a maiden century for New Zealand, fell at 85, off 77 balls, having shared a 130-run stand with Taylor.
Earlier tyro Devcich sparkled in an encouraging performance to give the innings the early impetus it needed.
"Obviously we are all very disappointed with the outcome of not just today's match but the whole series. To go down 3-0 was extremely disappointing, it definitely wasn't our plan when we came over here but you've got to hand it to the Bangladesh side, they played exceptional cricket today," Kyle Mills said after the defeat.
"There was a number of positives. Ross Taylor's innings today was a classy innings. He crafted it beautifully. Devcich and Tom Latham played their hands and I though Munro got an opportunity today and really grasped it with a magnificent knock. Throughout the series I thought Jimmy Neesham and Corey Anderson really stood up as well so young guys standing up is a good sign for New Zealand cricket and moving forward the next 15 months."
The game, frankly, was New Zealand's for the taking with a half decent bowling display. The series had already been lost, but they had a royal chance to regain some pride.
Instead the bowlers began badly, Bangladesh's openers, man of the match Shamsun Rahman and Ziaur Rahman belted 61 in 7.4 overs and the pace didn't let up. Shamsun, in his second international, rattled away to 96, rarely troubled.
Bangladesh's batsmen produced stands of 61, 65, 75 and 50 all in smart time to keep well ahead of New Zealand on the comparative run rate.
With Taylor and Luke Ronchi having smeared 73 in the last 5.2 overs, New Zealand's scoring rate soared towards the end, but Bangladesh had that covered too.
New Zealand's ground fielding was sub-standard, all the bowlers struggled to even get a consistency to their work.
Naeem Islam's 63 and Nasir Hossain's unbeaten 44 were important contributions and the win was achieved without captain Mushfiqur Rahim contributing with the bat.
He made just two, out to a brilliant one-handed catch above his head at square leg by Taylor. And consider Bangladesh's best player, world No 1 allrounder Shakib al Hasan missed the series with Dengue fever, and their dashing opener Tamim Iqbal sat out the final game.
This wasn't even Bangladesh's best XI. Grim times indeed for New Zealand.
SCOREBOARD
New Zealand
Anton Devcich c Razzak b Mahmudullah46
Tom Latham cMushfiqur b Rubel 43
Grant Elliott c Gazi b Razzak 3
Ross Taylor not out 107
Colin Munro c Mushfiqur b Mahmudullah 85
Corey Anderson c Ziaur Rahman b Sohag Gaz 1
Luke Ronchi not out 1
Extras: (3lb, 6w) 9.
TOTAL: (For five wickets) 307
Overs: 50.
Fall of wickets: 1-66, 2-82, 3-101, 4-231, 5-232.
Did not bat: Adam Milne, Nathan McCullum, Kyle Mills, Mitchell McClenagha.
Bowling: Mashrafe Bin Mortaza 8-0-73-0, Rubel Hossain 6-0-38-1 (5w), Sohag Gazi 10-0-67-1 (1w), Abdur Razzak 9-0-57-1, Nasir Hossain 10-1-33-0, Mahmudullah 7-0-36-2.
Bangladesh
Shamsur Rahman c Ronchi b Anderson 96
Ziaur Rahman c Milne b McClenaghan 22
Mominul Haque c & b Devcich 32
Mushfiqur Rahim c Taylor b N McCullum 2
Naeem Islam run out 63
Nasir Hossain not out 44
Mahmudullah c Ronchi b McClenaghan 16
Sohag Gazi not out 11
Extras: (4b, 3lb, 9w, 7nb) 23
TOTAL: (for six wickets) 309
Overs: 49.2.
Fall of wickets: 1-61, 2-126, 3-129, 4-204, 5-254,6-289.
Did not bat: Mashrafe Mortaza, Abdur Razzak, Rubel Hossain.
Bowling: Kyle Mills 8-1-55-0 (2nb), Adam Milne 7-0-42-0 (2w), Mitchell McClenaghan 9.2-0-69-2 (5nb, 1w), Corey Anderson 10-0-56-1 (4w), Nathan McCullum 8-0-44-1, Anton Devcich 7-0-36-1 (2w).
Toss: won by Bangladesh.
Umpires: Enamul Haque, Bangladesh, and REJ Martinesz, Sri Lanka
TV Umpire: Sharfuddoula, Bangladesh.