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Ibarguen, 32, who went on a 34-meeting unbeaten run after finishing second in London in 2012, won with her fourth round jump of 15.17m.
Her victory gives Colombia their second gold of the Games after weightlifter Oscar Figueroa.
Yulimar Rochas of Venezuela took silver with 14.98m and defending champion Olga Rypakova of Kazakhstan settled for bronze with 14.74m.
Colombian Caterine Ibarguen won the women's triple jump in Rio.