Having been kept on the field for longer than intended, South Africa eventually saw off their opponents at the Bay Oval to win the series with an unassailable 2-0 lead.
South Africa were asked to bat first after losing the toss, and Amla quickly found his form on the way to a crucial knock of 119 from 135 balls.
Amla's dismissal in the 45th over opened the door for the Kiwis as the hosts fought back to restrict the Proteas to 282-9 from their 50 overs.
However, New Zealand struggled in the early stages of their reply as their top six all departed without reaching 30 in Mount Maunganui.
Luke Ronchi - who was chasing down a maiden hundred - offered some resistance by clocking up 79 runs, until eventually slicing the ball which allowed De Plessis to collect a well-judged catch.
The sides face off once more on Sunday in the third ODI.