Put in to bat by the Kiwis, Afghanistan got off to a brisk start with openers Hazratullah Zazai and Noor Ali Zadran adding 66 runs by the 11th over.
But Neesham and Ferguson grabbed four wickets for four runs to reduce Afghanistan to 70-4.
They never recovered and lost wickets steadily before being bowled out for 172 with nearly 10 overs to spare.
Neesham was the pick of the New Zealand attack, grabbing five wickets for 31 runs while Ferguson picked up four wickets for 37 runs.
Hashmatullah Shahidi top-scored for Afghanistan with 59 runs off 99 deliveries.
New Zealand won their opening two matches of the tournament while Afghanistan lost their first two games.
(Reporting by Saikat Chatterjee, editing by Ed Osmond)
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