The visitors kept themselves alive when five-eighth Raecene McGregor scored, before Moran's match-winning one-pointer.
The result gives Australia their second straight World Cup final win over New Zealand, after they ended 13 years of dominance by the Kiwi Ferns with a historic tournament victory in 2013.
It was also the fourth straight loss New Zealand have suffered at the hands of the transtasman rivals this year, after the Jillaroos enjoyed a three-nil series win at the Auckland Nines and an Anzac test win in May.
The defeat leaves a bitter taste in the mouth of retiring Kiwi Ferns captain Laura Mariu, who played in all five World Cups, while New Zealand also farewelled 40-year-old veteran squad member Sharlene Atai.
Australia looked sluggish early but soon clicked into gear with back-rower Renae Kunst offloading inside to fullback Nakia Davis-Welsh who found Kelly for their first try after eight minutes.
New Zealand's reply came swiftly on their next visit downtown, with McGregor throwing a beautiful long cut-out ball for Hireme to run in her first, with Kimiora Nati's conversion levelling the scores.
The Kiwi Ferns continued to build pressure by constantly sending their big forwards at Moran, while her halves partner Ali Brigginshaw struggled with her last-tackle plays.
New Zealand then capitalised on two errors from Australian wing Chelsea Baker, when she spilled a cross-field kick near the line before being brushed aside by Hireme off an attacking scrum, with the visitors taking a 10-6 lead at the end of the first quarter.
The Jillaroos fought back and found reward with Moran stepping through and carrying three defenders over the line, before booting her second conversion to reclaim a two-point advantage for her side before the break.
Both teams had chances early in the second half but the Jillaroos came up trumps when Brigginshaw's grubber bounced into the hands of a chasing Kelly to score her second inside the last half hour.
Three minutes later they were in again when Walton barged her way over to plant the ball down, with Moran's conversion giving the hosts an unassailable lead.
The Kiwis persisted and ensured a frantic finish when a damaging run and offload from bench forward Krystal Murray put McGregor over, but it was all too late.
