Having hit an all-time low of 117th as recently as 2011, Wales initially began their resurgence under the leadership of the late Gary Speed.
A minor slide followed the appointment of Chris Coleman as Speed's successor, but the former Fulham and Real Sociedad boss has led his players to second in Group B at the midway point of Euro 2016 qualifying.
It was a 3-0 win in Israel that earned Wales their leap in the rankings, but next up for Coleman's men is the visit of group leaders Belgium, who climbed above Colombia to third.
Brazil and Uruguay also made gains, while Spain and Switzerland return to the top 10 at the expense of France and Italy.
Bhutan, meanwhile, make the biggest jump, climbing 128 places to 163rd in the world.
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