Substitute Ben Waine scored the winner in his first senior international game for New Zealand from a free kick in the 75th minute.
The Wellington Phoenix player had only been on the field for less than 10 minutes when he scored from close range.
Papua New Guinea had not played an international fixture since 2019, whereas the All Whites last played in January.
The Kapuls are ranked 165 on Fifa's ranking, more than 50 places below New Zealand (111).
New Zealand had several chances to score late in the game but could not convert.
The All Whites' next game of the tournament in Group B is against Fiji on Tuesday, followed by New Caledonia on Friday.
The top two sides from Group B will be face the top two out of Group A which includes Solomon Islands, Tahiti, Vanuatu, and the Cook Islands in the semi-finals on 28 March.
The final is on 31 March and the winner advances to an intercontinental playoff in June - a match likely to be against Costa Rica or Panama to book a place in the Football World Cup in November in Qatar.