Ish Sodhi was again a revelation, creating the stumping of Soumya Sarkar with a regulation leg spinner, followed by a disguised googly to bowl the veteran Mahmudullah and eventually crashing a ball into the stumps of No.11 Al-Amin Hossain.
He took three for 21 from 3.4 overs but was complemented by the left-arm orthodox spin of Mitchell Santner, the off spin of Nathan McCullum and Grant Elliott's hypnotic change of pace with saw the latter finish with three for 12.
The fielding set the tone - Colin Munro rifled in a direct hit to remove Tamim Iqbal in the second over.
The Black Caps struggled to gain batting momentum, but their total of 145 for eight always looked competitive on an unresponsive wicket after captain Kane Williamson won the toss and opted to don the pads for the fourth consecutive pool match.
Led by Williamson's 42 off 32 balls, the New Zealanders realised a recalibration was required in the conditions, as the ball bobbed up off sluggish clay. However, the loss of four wickets for 27 in the final three overs resulted in more of a plod than a sprint at the end.
They only scored one boundary between the sixth and 13th overs, but the circumstances needed patience to trump aggression.
The move to play three spinners again, as they did in the victory over India in Nagpur, was prescient. Bangladesh's quick bowlers got about as much carry as a middle-aged man marking out the long run for beach cricket after Christmas lunch.
They were far better taking the pace off the ball. Mustafizur Rahman starred with the wickets of Henry Nicholls, Williamson, Elliott, Santner and McCullum in his allotment, finishing with five for 22. Even those figures were distorted by his final hat-trick ball being hit for six by Mitchell McClenaghan.
Those are the best figures at the tournament.
The highlight was his dismissal of Williamson who moved in front of off stump to lap the ball behind square, but was deceived by the lack of pace. Rahman received support from Hossain (two for 27) and captain Mashrafe Mortaza (one for 21 from three overs).
Williamson and Ross Taylor (28 off 24) were the only batsmen to demonstrate relative comfort. Williamson took on more of an aggressive role after the decision to rest Martin Guptill's tender hamstring and offer Nicholls a debut.
Taylor was dropped by Hossain at deep backward square leg on nine in the 16th over to bring up the New Zealand 100.
Colin Munro (35 off 33) eventually found rhythm, but avoided a plumb lbw shout from left-arm orthodox spinner Shakib Al-Hasan to umpire Johan Cloete when he was eight in the 10th over.
In 60 years of playing in India, New Zealand had only appeared in two tests (1955 and 1965) and a one World Cup one-dayer versus Zimbabwe in 1987 at Kolkata before today.
