Blanchett, 44, was the favorite to win this year's Oscar after sweeping awards season with prizes including the Golden Globe, Screen Actors Guild and BAFTA earlier this year.
Blanchett beat Amy Adams, Sandra Bullock, Judi Dench and Meryl Streep for the Oscar.
"As random and subjective as this award is, it means a great deal in a year of, yet again, extraordinary performances by women," Blanchett said in her acceptance speech.
She added that while there are still some people in the film business "who are still foolishly clinging to the idea that female films with women at the center are niche experiences. They are not. Audiences want to see them, and in fact, they earn money."
Including "Blue Jasmine," Blanchett has been nominated for an Oscar six times in a 20-year career that spans stage and film in Hollywood and Australia and both drama and action.
Blanchett won the best supporting actress statuette in 2005 for her role as Hollywood icon Katharine Hepburn in "The Aviator." Previous Oscar nominations came from her role as Britain's Queen Elizabeth I in "Elizabeth" and "Elizabeth: The Golden Age."
In "Blue Jasmine," Blanchett's character, Jasmine, loses everything, including her mind, thanks to her husband's financial and marital misdeeds and her own hapless ways.
The film is a cautionary tale of what happens when a woman builds her life around a wealthy husband, unaware of the house of cards in which she lives.
The film was Blanchett's first with Allen, who is known for creating memorable female characters like Diane Keaton's Annie Hall. (Reporting by Nichola Groom and Lisa Baertlein, editing by Jill Serjeant)
Phot credit: Darren Decker / ©A.M.P.A.S.