The Pukpuks only led by 5-3 at half-time, with replacement Emil Latumahina scoring the opening try minutes after coming onto the field to replace injured second five Tisa Kautu, but scored four more tries in the second spell, including in the final play of the match, to end up comfortable winners.
PNG captain Ahulo Ottio said they started slowly but eventually found their rhythm as the match wore on.
"We knew it was always going to be a grind with the bulk of the boys (in the Niue team) coming from New Zealand and Australia," he said.
"Happy that we stuck to our process and I think we panicked a bit in the first half but we regained that (control) in the second half and just happy to come away with the win."
Niue skipper Luka Gibbs said there were some good signs in the first half but they failed to capitalise on a series of chances.
"It was definitely a hard, physical game - fast game. It was what we expected," he said. "Hats off to our team, we put everything we had out there.
"We didn't come away with the result that we wanted - I guess a few missed opportunities - but the game could have gone either way. Full credit to PNG: they're definitely a good side and we knew they'd be a hard nut to crack."
Papua New Guinea will face Solomon Islands in the final round of matches on Saturday, who thrashed Nauru 61-7 in the earlier kickoff to secure their first win of the tournament.
Second five Chris Saru scored the Solomons' opening try with less than 60 seconds on the clock. The Melanesian side doubled their lead to 10-0 a few minutes later before openside flanker Amram Fulton burrowed over the line from close range to score Nauru's second ever international try and cut the deficit to 10-7.
Solomon Islands quickly re-established their dominance with another four first half tries to lead 30-7 at the interval before touching down for five further tries in the second spell.
PNG have the maximum 10 points from two matches and will secure a fifth Oceania Rugby Cup title if they can beat Solomon Islands in Saturday's final round, while a bonus point should also be enough to finish on top thanks to a far superior points differential.
Solomon Islands have six points from two games and need to beat the Pukpuks with a four-try bonus point and ensure the hosts don't earn a bonus point if they are to lift the title for the first time.