Kane Williamson struck an unbeaten 79 which guided his side to a seven-wicket win over Afghanistan.
The Black Caps were off to the worst possible start when Aftab Alam had Martin Guptill caught on the first ball of the innings.
Afghanistan were without their premier spinner Rashid Khan, who was struck on the head by Lockie Ferguson's bouncer in the first innings.
He walked off the field and failed his concussion test, ruling him out for the rest of the match and depriving Afghanistan of their ace spin bowler.
Afghanistan vs New Zealand Highlights
Aftab Alam lead the Afghan attack in Rashid’s absence as he removed Colin Munro to leave New Zealand on 41-2.
Williamson rode his luck when he only made his ground in a run-out review.
Williamson alongside Ross Taylor steadied the innings in an 89-run partnership.
The duo picked up singles and scored an occasional boundary until Taylor was knocked over by Aftab Alam for his 48 off 52 balls.
New Zealand then reached the target comfortably in 32.1 overs.
Earlier, Neesham turned around the fortunes for the Kiwis with his impressive medium pace bowling.
Asked to bat first, Hazratullah Zazai and Noor Ali Zadran smashed a 66-run partnership.
But Hazratullah smashed one straight to Colin Munro at deep cover off Neesham’s bowling.
Skipper Gulbadin Naib failed with a review to overturn the decision for his edge behind as Afghanistan lost four wickets for four runs in a span of 21 balls.
Hashmatullah Shahidi (59) top-scored for Afghanistan, but Neesham and paceman Lockie Ferguson, finished with four wickets.