The left-hander smashed 10 boundaries and three sixes while Hashim Amla made a 40-ball 41 after South Africa were put in to bat by New Zealand at Zahur Ahmed Chowdhury stadium.
Duminy was not out for 86 while Albie Morkel finished with 13 off eight deliveries as South Africa added 70 in the final five overs.
South Africa's start wasn't ideal as they lost opener Quinton de Kock (four), Faf du Plessis (13) and AB de Villiers (five) inside seven overs with the score at 42.
It was Amla and Duminy who steadied the innings during their 55-run fourth wicket stand to give some respectability to the total.
Amla was finally out in the 14th over as his drive hit the non-striker batsman Duminy's bat and looped in the air for Corey Anderson to take the catch off his own bowling.
Anderson was the best New Zealand bowler with 2-28.
South Africa were lucky to get their captain Du Plessis back after he missed the five-run defeat against Sri Lanka in the first match.
He replaced Farhaan Behardien in the team while New Zealand remained unchanged from the side which beat England via Duckworth-Lewis method.
The top two teams from each of the two groups will qualify for the semi-finals.