The victory, which gave the hosts a 3-0 series win, was, however, not as easy as in the first two ODIs, as the tourists, who put up 241 for 9 after being inserted in, were competitive right through.
An impressive maiden One-day hundred by Imrul Kayes, who hit 101, helped Bangladesh to a fighting total before skipper Shakib Al Hasan starred with the ball, claiming four wickets for 33.
But those efforts were not enough in the wake of Guptill's run-a-ball onslaught, comprising nine fours and three sixes. By the time he departed New Zealand were 195 for 5 with 15 overs left.
Though two more wickets fell for 15 runs -- Neil Broom bowled for 18 by Al Hasan and Jacob Oram [ Images ] (12) offering a soft catch on 12 -- Ian Butler (13 not out) and James Franklin (19 not out) avoided any hiccups and took the Kiwis home from 210 for 7 with 31 balls to spare.
New Zealand won the first ODI by 146 runs and the second by five wickets.
The teams meet next in a one-off Test, starting in Hamilton on Monday.
Tamim Iqbal b T Southee 8
Imrul Kayes b D Vettori 101
Aftab Ahmed c T Southee b AJ McKay 18
Mohammad Ashraful [ Images ] c B McCullum b J Oram 31
Shakib Al Hasan c R Taylor b T Southee 36
Mushfiqur Rahim lbw b D Vettori 4
Mahmudullah b D Vettori 6
Naeem Islam c P Ingram b T Southee 10
Shahadat Hossain run out (P Ingram/B McCullum) 4
Shafiul Islam not out 2
Rubel Hossain did not bat
Extras: (B 4, LB 3, W12, NB 2) 21
Total: (for 9 wickets in 50.0 overs) 241
Fall of wickets: 1-8, 2-41, 3-99, 4-183, 5-205, 6-221, 7-234, 8-234, 9-241.
Bowling: Southee 10-2-37-3, McKay 8-0-48-1, Butler 8-0-58-0, Oram 6-1-23-1, Vettori 10-0-42-3, Franklin 5-0-18-0, Guptill 3-0-8-0.
B McCullum b Rubel Hossain 19
P Ingram b Shakib Al Hasan 25
M Guptill c Tamim Iqbal b Shakib Al Hasan 91
R Taylor st Mushfiqur Rahim b Shakib Al Hasan 3
D Vettori c Aftab Ahmed b Mahmudullah 34
N Broom b Shakib Al Hasan 18
J Oram c Shakib Al Hasan b Naeem Islam 12
J Franklin not out 19
I Butler not out 13
T Southee did not bat
A McKay did not bat
Extras: (B 0, Lb 6, W2, NB 2) 10
Total: (for 7 wkts in 44.5 overs) 244
Fall of wickets: 1-37, 2-75, 3-89, 4-160, 5-195, 6-204, 7-210.
Bowling: S Hossain 5.5-0-39-0, S Islam 8-1-46-0, R Hossain 10-0-55-1, S Al Hasan 10-0-33-4, N Islam 8-0-32-1, Mahmudullah 3-0-33-1.