Victory secured country the 12th and final place at the ICC Trophy which takes place in Ireland in July from which the top five sides will qualify for the World Cup in the West Indies in 2007.
Heavy overnight rain restricted the final to 33 overs-a-side.
Batting first, PNG made 176 all out in 32.4 overs with the crucial contributions coming from Jamie Brazier, who hit 62 from 43 balls, and Arua Uda with 57 from 64 balls.
The target proved too much for Fiji who crumbled to 146 all out from 31.5 overs.
Neil Maxwell top scored again for Fiji with 56 runs from 42 balls whil Inoa Baeau (3 for 28) and Toka Gaudi (2 for 12) did the damage with the ball.
Man of the Match Brazier was delighted with his team's victory and said that World Cup qualification was now a realistic goal for his side.
"It is great to play against teams from throughout the world and fantastic to finish the event as winners," said Brazier.
"I think that the key to our success was that we fielded better than anyone else and we ran well between the wickets even in the heat. We prepared well for this event and its pleasing to have the effort rewarded.
"The next step is to work even harder ahead of the ICC Trophy. Some people didn't give us a chance in this event so, who knows, we could even make it to the World Cup."