Ogier had taken control of the rally on Friday afternoon, when he burst clear of what had started off as a super-close tussle involving the World Rally Championship leader's Volkswagen, M-Sport Ford team-mates Neuville and Mads Ostberg, and Citroen's Mikko Hirvonen.
All led at various junctures and the lead group was often covered by just seconds.
But as Ogier settled he was able to raise his game, and by the start of the final morning he was nearly 40s clear.
He declared that he would take it easy through Saturday, but still set a new record time on the legendary Ouninpohja stage.
Hirvonen lost touch with the leaders when he caught the worst of a storm on the Himos stage on Thursday afternoon, so that left Neuville and Ostberg to battle for second.
The two young drivers gave it everything, swapping positions four times on Saturday morning alone.
Their battle was not settled until the penultimate stage, when Ostberg slewed off the road and spun while avoiding a rock, finally giving Neuville some breathing space.
Neuville then celebrated his second place with the fastest time on the power stage.
The eventual Ogier, Neuville, Ostberg top three made this only the second ever Rally Finland not to feature a Finn on the podium. The Markko Martin, Petter Solberg and Richard Burns podium of 2003 was the only other occasion.
Hirvonen was top Finn in fourth, but was overshadowed in the Citroen camp by WRC returnee Kris Meeke.
Recruited for one rally only to stand in for Khalid Al-Qassimi, Meeke was rapid from the outset, shrugging off a blocking spat with Evgeny Novikov to keep Hirvonen in sight until the final morning.
Meeke was set for fifth, only to crash out with one stage to go.
That incident and a late retirement for Jarkko Nikara - who had got Prodrive's revived Mini up to sixth - brought Dani Sordo into the top six.
The works Citroen driver had a muted rally and was a long way off the pace all weekend as he struggled for confidence.
Novikov recovered from the crash that ended with him rejoining in Meeke's path to take seventh.
Jari-Matti Latvala had his heart set on victory following encouraging recent results, only to damage his VW's suspension on only the second stage, wrecking his weekend.
WRC2 had a home winner in the shape of Jari Ketomaa. The Finn dominated from the outset, while Robert Kubica impressed with a clear second place in class on his debut on this famous event.