Inspired by Real Madrid’s Gareth Bale, they were the biggest movers at the top end of the list with 153 points ahead of the April rankings after beating Israel 3-0 in their Euro 2016 qualifier in Haifa.
Meanwhile, England have climbed three places to 14 after beating Lithuania in Euro 2016 qualifying and drawing a friendly in Italy last month, while Scotland are up 10 spots to 29.
Northern Ireland are up one to 42 and the Republic of Ireland have climbed four places to 62.
Belgium rose to its highest-ever spot at No 3 in the rankings, which are still led by World Cup winner Germany followed by Argentina.
Brazil, who beat France in a friendly last month as their resurgence under new boss Dunga continues following their embarrassing exit from the World Cup, rose to No 5 and swapped places with the Netherlands at No 6.
Switzerland and Spain return to the top 10, at nine and 10, respectively.
Costa Rica fell two spots to No 15 but still lead CONCACAF nations. Mexico rose three positions though to No 18 while the United States climbed five places to be 27th.
Seeding for the European qualifying groups will be decided by the July rankings ahead of the July 25 draw in St. Petersburg, Russia.