Their tour started well with a hefty 63-30 win over Japan in Yokohama, followed by a 29-21 victory against Wales in Cardiff, but back-to-back defeats to England and Scotland means they have lost their status as one of the world's top three sides.
The switch between Ireland and Australia is one of two changes in the top 10 of the world rankings, with France slipping to a record low of ninth.
The 2023 Rugby World Cup hosts have endured a shambolic 2017 season under the tenure of coach Guy Noves, and that didn't change during the end-of-year test window.
Losses to the All Blacks and Springboks was followed by an embarrassing 23-all draw with Japan at the newly-constructed U Arena in Paris last weekend.
France's winless run in November means they have not tasted success since their bizarre 20-18 victory over Wales during the Six Nations in March, and will have to wait until next year's tournament to register a win.
Despite Argentina's equally poor 2017 campaign, in which they won only two of their 12 tests, the Pumas have claimed eighth spot ahead of the French.
Outside of the top 10, the biggest climber on the rankings was Chile, who were promoted three places to 24th following their 32-10 win over Germany in Offenbach.
The biggest fallers were Moldova, plummeting five spots to 46th as a result of their 22-20 loss to Switzerland in the Rugby Europe Trophy competition.
With the Springboks' test against Wales the only clash between tier one nations this upcoming weekend, there is potential for one last change in the top 10 before the 2017 international season draws to a close.
Allister Coetzee's men could force the Wallabies further down the pecking order with a win in Cardiff on Sunday morning (NZT), while Wales would close the gap on sixth-placed Scotland with a victory at the Principality Stadium.
World Rugby Rankings as of 27 November 2017:
1 - New Zealand (93.99 points)
2 - England (90.87)
3 - Ireland (86.39, up one place)
4 - Australia (85.49, down one place)
5 - South Africa (84.90)
6 - Scotland (84.11)
7 - Wales (80.98)
8 - Argentina (78.22, up one place)
9 - France (78.09, down one place)
10 - Fiji (77.93)
11 - Japan (75.66)
12 - Georgia (73.46)
13 - Tonga (71.87, up two places)
14 - Italy (71.25, down one place)
15 - Romania (69.58, down one place)
16 - Samoa (69.03)
17 - USA (66.87)
18 - Uruguay (65.63)
19 - Russia (64.45)
20 - Spain (61.68)