Bangladesh blunders gift New Zealand ODI series win
Black Caps skipper Tom Latham scored an unbeaten 110 after being dropped twice with New Zealand chasing 272 at Christchurch's Hagley Oval.
"We should have won this game. We created chances but we just couldn't hold on to those dropped catches," he said.
"We hardly ever win games but in this kind of situation we have to make sure that we do everything 100 percent. I'm disappointed."
Tamim top-scored for the tourists with 78 and Mohammad Mithun contributed an unbeaten 73 off 57 balls.
Latham's 110 came off 108 balls and was his fifth ODI century, while Devon Conway's 72 helped anchor the innings.
Tamim had demanded a better performance from his players after they were skittled for 131 in the opening match and slumped to an eight-wicket defeat.
Signs did not look promising when opener Liton Das departed for a duck in the second over.
But Tamim and Soumya Sarkar preserved their wickets, grinding out an 81-run partnership at an agonisingly slow run rate to lay the foundation for a big finish.
Soumya was stumped on 32 trying to lift the run rate as Tamim brought up his 50th ODI half-century off 84 balls after surviving two umpiring reviews.
His luck ran out trying to pinch a quick single, when Neesham showed impressive soccer skills to kick the ball into the stumps side-on and dislodge the bails.
New Zealand began briskly in reply despite the early loss of opener Martin Guptill for 20.
A double strike from spinner Mahedi Hasan applied the brakes to the run rate, forcing Conway and Latham to rebuild.
The bowlers obliged but errors in the field meant chances went begging and momentum shifted back to New Zealand.