Nicholls then anchored the innings with a composed 68 off 83 balls, hitting nine fours for his 17th ODI half-century. The 34-year-old stitched together useful partnerships with Will Young (30) and captain Tom Latham (14) to steady the innings after the early setback.
Young survived an early drop on one off Shoriful but fell to leg-spinner Rishad Hossain while attempting a reverse sweep, edging to slip.
Rishad struck again soon after, dismissing Nicholls with another failed reverse sweep to leave New Zealand under pressure.
Latham and Muhammad Abbas failed to build on the platform, but all-rounder Dean Foxcroft counter-attacked with a brisk 59 off 58 balls, featuring eight fours, to lift the visitors past 200. He was eventually bowled by Nahid Rana attempting a yorker-length delivery.
Nathan Smith’s unbeaten 21 off 22 balls provided a late boost as New Zealand reached a competitive total.
Shoriful finished with 2-27, while Taskin Ahmed and Rishad Hossain claimed two wickets apiece for Bangladesh.
In the chase opener Saif Hassan made 57 while handy scores from middle order batsmen Towhid Hridoy (55), Litton Das (46) and Afif Hossain (27) saw Bangladesh at 184-4 before they lost their final six wickets for 37 runs.
Tickner took the last four wickets.