Warren Gatland's injury-hit Welsh stunned England by fighting back to win 28-25 with a converted Gareth Davies try and Dan Biggar penalty in the last 10 minutes and are at their highest position since the rankings began in 2003.
England, now faced with a tough task to qualify from Pool A, dropped three places.
New Zealand remain top of the pile, while Australia, who face England on Saturday in a pivotal clash, drop from two to three.
Six Nations champions Ireland are fourth and South Africa, who bounced back from their shock defeat against Japan to beat Samoa at the weekend, are at five.
Scotland's back-to-back wins over Japan and the United States have lifted Vern Cotter's team three places to nine.
(Reporting by Justin Palmer; Editing by David Goodman)
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