The comedy is a first for Inarritu, 51, who is, otherwise, known for his serious dramas like "Amores Perros", "21 Grams", "Babel" and "Biutiful".
The director earlier won the best original screenplay trophy that he shared with co-writers Nicolas Giacobone, Alexander Dinelaris Jr and Armando Bo.
The film is a visually complex story that was shot mostly in long shots that were blended later to give the feeling of continuity and required maximum dedication from its actors, cinematographer and Inarritu.
"Birdman" tells the story of Riggon Thomson, a jaded movie star who is otherwise famous for having played superhero Birdman on-screen.
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Thomson, still dying to achieve the critical acclaim that eluded him in his younger days, decides to mount an ambitious Broadway play but things take a bizarre turn when his superstar ego and self doubt collide.
The Mexican helmer was previously nominated for best director and picture in 2006 for "Babel". Birdman's other win of the night was in cinematography.
"Birdman" was a long-gestating story that Inarritu decided to shoot when his project "Revenant" with Leonardo DiCaprio got delayed.