Second place would have been Ireland's highest ever ranking position since the process began back in 2003.
The only other move in the world's top 10 sees Scotland swap places with Wales, the team they beat 21-9 at Murrayfield on Saturday.
The Scots are now up to eighth place, 1.02 rating points ahead of Wales in ninth. They lie 1.78 ratings points behind England in seventh, who failed to overhaul Argentina in sixth despite recording a hard-fought 20-7 victory over Italy at Twickenham.
IRB WORLD RANKINGS: (Issued on February 12)
1 - New Zealand 94.59 rating points
2 - France 87.17
3 - Australia 85.55
4 - South Africa 84.71
5 - IRELAND 83.99
6 - Argentina 79.61
7 - England 79.48
8 - Scotland 76.78
9 - Wales 75.74
10 - Samoa 73.86
