The Kumuls now lead Fiji 2-1 in their fledgling international careers.
Jarryd Hayne played at halfback for Fiji for the first time and kept PNG pegged back with good, tactical kicking early, but his team was starved of possession with loose play in possession.
The Parramatta centre did manage to roll a grubber into the north-western corner in the 53rd minute for Marcelo Montoya to ground.
But the 2017 World Cup semi-finalists were not at their creative best, limiting the number of offloads the Fijians are usually famous for and making too many handling errors.
In contrast to the lack of direction by the Fiji halves, PNG's five-eighth Lachlan Lam – son of Sydney Roosters and Queensland Origin legend Adrian Lam – continually asked questions with his passing and kicking games.
PNG had just five players with NRL experience in their line-up compared with 10 for Fiji. But that didn't stop the Kumuls racing to a 12-0 lead after 17 minutes, through tries to winger Junior Rau and prop Luke Page.
Rau was on debut for PNG after being called into the side when Dragons winger Nene Macdonald was ruled out through injury (shoulder).
A penalty for Eloni Vunakece hitting PNG kicker Watson Boas late pushed the score to 14-0. Rau collected his second in the 36th minute off a Justin Olam flick pass, and then Olam raced 45 metres, off a James Segeyaro pass, to score under the posts in the 39th.
The propelled the Kumuls to a 26-4 half-time lead – four tries to one.
The Fijians finally got on the scoreboard in the 32nd minute when centre Tyrone Phillips stepped off his right foot, outfoxing two defenders, to cross.
The first-half completion rate told the story of lopsided possession. Fiji were 10 from 14 sets, while PNG not only enjoyed seven more sets but completed at 86% (18 from 21).
Fiji had two tries disallowed in the first 10 minutes of the second-half, which didn't help their spirits, with Melbourne Storm winger Suliasi Vunivalu scoring a consolation try with 12 minutes remaining.