Bangladesh won by five wickets with 10 balls to spare; the first time they had triumphed in 17 ODIs against New Zealand away from home.
The Black Caps' middle order betrayed the momentum created by Tom Latham and Neil Broom's 133-run second-wicket stand.
They went from 208 for three in the 39th over to 226 for seven in the 44th. Anderson's dismissal for 24 triggered the loss of four wickets for 18 runs in 27 balls as Neesham, Santner and Munro followed.
The New Zealand bowlers could not defend for any sustained period as a result, raising questions over their penetration. Anderson took none for 37 from five overs; Neesham took none for 28 off four; and Santner took one for 53 from 10 but could not find the rhythm of his previous three matches, which included a career best five for 50 against Ireland.
The required run rate fluttered above six, but the Bangladeshi batsmen hardly swung like bushmen with machetes at the death.
The side's batting capability will draw scrutiny against Australia and England next month.
Santner is expected to start alongside Jeetan Patel in the pool matches at Birmingham and Cardiff. Presuming Neil Broom returns to No.5 and incumbent captain Tom Latham wins an opening spot - and the wicketkeeping gloves - from Luke Ronchi on the basis of batting form, that leaves space at Nos 6 and 7 for two of Anderson, de Grandhomme and Neesham.
Neesham's been a superb ODI batsman this year with 274 runs at an average of 34.25 and strike rate of 99. He has let himself down on occasion with the ball, taking four wickets at an average of 61, strike rate of 56 and economy rate of 6.59.
De Grandhomme's only batted three times in 2017 for an average of 100 and strike rate of 99. He has taken four wickets at 25.75 with each coming every 36 balls. He has conceded 4.29 runs per over. Since returning to the ODI side in December he has not passed 34 not out in six innings, nor taken more than two wickets in the format.
Anderson is similarly affected by a small sample size as he returns from a summer injury lay-off. He scored 20 and 24 respectively against Ireland and Bangladesh at a strike rate of 79 alongside two wickets in nine overs at an economy rate of 5.77. He has not passed 35 or taken more than two wickets in an ODI since the World Cup semi-final.