Belgium and France had been tied at the top last month and while both sides won one game and drew another in October, the Belgians, with 1,733 points, moved ahead by a single point under the formula for calculating the rankings.
Belgium beat Switzerland in the Nations League and drew with the Netherlands in a friendly. World champions France defeated Germany in the Nations League and were held by Iceland in a friendly.
Brazil, one of only two non-European sides in the top 10 along with Uruguay, remain third, followed by Croatia and England.
Gibraltar, who only became FIFA members in 2016, rose eight places to their best ranking of 190th thanks to the their Nations League wins in Armenia and at home Liechtenstein.
Madagascar, who earlier this month qualified for their first African Nations Cup finals, climbed into the top 100 for the first time since 2002. They were ranked 100th.
Tunisia, 22nd, were the highest ranked African team and Iran, 30th, the top Asian side.
(Writing by Brian Homewood; Editing by Peter Rutherford)
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