Garfield played Desmond T Doss in the Mel Gibson-directed movie, while Washington essayed the role of Troy Maxson in his own directorial.
The nomination for the two-time Oscar-winner, Washington, comes after he recently opened up about experiencing the lack of diversity at the Academy firsthand.
Nominated under the same category alongside Garfield and Washington, Viggo Mortensen's Oscars nod for his understated performance in "Captain Fantastic" too came as a surprise.
Actor Michael Shannon, who received a nomination for the best actor in a supporting role for Tom Ford's "Nocturnal Animals, was another unpredicted choice.
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Best Picture recognition for "Hell or High Water" alongside "Arrival", "Fences", "Hacksaw Ridge", "Hidden Figures", "La La Land", "Lion", "Manchester By the Sea" and "Moonlight" also surprised award pundits.
On the other hand, Actress Amy Adams, who got critical acclaim for her performance in "Arrival", failed to get nomination despite the movie bagging eight nominations, including best picture and director.
Director Martin Scorsese, the man with 12 Oscar nods (and lone win to date) in his 50-year long career, was unable to notch any recognition for his film "Silence", which just bagged one nomination for best cinematography.
Biographical drama, "Sully", directed by Clint Eastwood was thought to be a major contender but lost steam in the race. It was also overlooked by the Academy in the best picture category. Its leading man and two-time Oscar-winner Tom Hanks too did not get the nomination.
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