The Eagles dropped to 34, from its previous position of 33. The ranking makes them the third placed team in Africa.
The Falcons rose to the 36th position from the 38th they were last month.
Within the month under consideration, the Eagles played only one friendly game, losing a two-goal lead to draw 2-2 with Ukraine in Dnipro on September 10.
The Falcons played two games: their 2-0 and 1-0 wins over Algeria in the first and second legs of the 2020 Olympic Games qualifiers.
In the men’s category, Belgium maintained top position, while France moved up one place to replace Brazil as second.
England are unchanged in fourth, while Portugal displaced Uruguay in the fifth position, moving up from sixth.
Other teams in the top 10 are Spain, Croatia, Colombia and Argentina, who are placed seventh, eighth, ninth and 10th.
Senegal, who are the highest placed African team, remain unchanged in the 20th position, with Tunisia the second placed and 29th in the world.
Africa champions, Algeria, are fourth in Africa and 38th in the world; Morocco, fifth in Africa and 39th in the world; and Egypt sixth in Africa and 49th in the world.
Other top 10 African teams are Ghana, seventh in Africa and 51st in world, Cameroon, eight in Africa and 53rd in world; Ivory Coast, ninth in Africa and 56th in the world; and Mali, 10th in Africa and 57th in the world.
In the women’s category, the first two remained unchanged, with world champions, USA, maintaining their top spot ahead of Germany.
Holland, France, England, Sweden, Canada, Australia, South Korea and Brazil are the other teams in the top 10.