It is the highest position that Wales have achieved since the rankings were launched last October.
New Zealand, meanwhile, strengthened their grip on the top spot after their second substantial win over England in consecutive weeks.
If England lose to Australia by more than 15 points in Brisbane next Saturday, the extra ratings points gained by the Wallabies for that margin of victory will see them take second place from the world champions.
Australia's victory over Scotland did not affect either team's rating as the ratings gap between them was too big.
South Africa consolidated fifth place in the rankings by defeating Ireland for the second week running.