It is a six-year high for Michael O’Neill’s side who defeated the Faroe Islands 3-1 and drew 1-1 with Hungary last month to remain in the box-seat to qualify for next summer’s Euro finals.
Wales are just one place behind Brazil after reaching an all-time high of eighth in the latest rankings.
They stay above England, who remain at 10th, while Scotland are down nine to 40th and the Republic of Ireland slip three places to 54th,
World Cup winners Germany have moved back into second place in the rankings behind Argentina.
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The new list takes into account the Euro 2016 qualifiers in September.
Northern Ireland sit top of Group F with two games remaining against Greece and Finland.