Sunderland midfielder Katie Kitching scored the only goal of the match in the 55th minute, sending the Kiwis to the World Cup for the seventh time.
Papua New Guinea still have a chance to qualify through an inter-continental playoff during the international window in November or December.
New Zealand were twice denied by VAR, four times by the woodwork and repeatedly by Papua New Guinea goalkeeper Betty Sam, who was outstanding in a hard-working defence.
Deven Jackson appeared to have scored from Rebecca Stott's through ball in the 32nd minute but the VAR showed Jackson had been caught by PNG's offside trap.
New Zealand were awarded a penalty in first-half stoppage time after Maya Hahn was brought down in the box, but the decision was overturned after the officials considered replays for more than five minutes.
New Zealand's finishing let them down on numerous occasions, notably when Jackson missed an open goal in the 51st minute.
"It's amazing. We had a job that we had to get done tonight and we did what we needed to do to get the result," New Zealand coach Michael Mayne said.
"We're over the moon with going to the World Cup and now we can plan and see what we have to do this year to get ready for the World Cup.
"At half-time we spoke about our finishing. Frustration had to be tempered. We were creating, we felt a goal was going to come and it was one of those games in which we had opportunities but weren't clinical when we needed to be."
Papua New Guinea didn't have a shot on goal but their defence was superb. They earned their place in the final with a 1-0 win over giant-killers American Samoa while New Zealand beat Fiji 5-0 in the semi-finals.
"I'm very proud of the girls," Papua New Guinea coach Ericson Komeng said.
"We weren't clinical enough tonight to compete with New Zealand but I'm proud of the girls for all the hard work they put in today.
"We just have to go back and work on little things and get ready for the playoff."
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