In terms of being recognised by the academy for best picture, only six have been nominated:

The Exorcist, Jaws, The Silence of the Lambs, The Sixth Sense, Black Swan, Get Out.

The other 5 did win awards at the academy as well, though (rightfully so). Out of those six, The Silence of the Lambs was the only winner and dominated winning 5 Oscars in 1992. So that's the prime example.

Still is a pitch-perfect film. The origin of how Demme picked Goodbye Horses (a melancholic banger of a song) juxtaposed to how it was incorporated in the film where Ted Levine acts in one of many scenes that makes the skin crawl is pretty amazing.