Ireland, who beat Argentina 28-19 at the weekend, have pushed the Wallabies down to fourth place after Michael Cheika's side were thumped 53-24 by the Scots.
The defeat was Australia's biggest-ever loss to Scotland at Murrayfield, with the home team given a huge advantage after Wallabies prop Sekope Kepu was sent off just before halftime for a shoulder charge to the head.
It was Australia's second-straight defeat after going down to England 30-6 the week before.
The All Blacks' victory over Wales saw them maintain their advantage over England at the top of the standings heading into the new year, while the Pumas overtook France in eighth.
World Rugby rankings
1. New Zealand
5. South Africa
Photo by: CRAIG BROUGH/REUTERS. Caption: Dejected Australian players leave the pitch following their heavy defeat to Scotland.