When making the 1976 film “A Star Is Born,” Barbra Streisand, still in the novice stages of learning to play guitar for the movie, brought a few rough chords to the lyricist Paul Williams.

He said he was struck by the “sweet, innocent beauty” of the melody, which eventually became the award-winning song “Evergreen.”

“She went ‘da-da-de-da,’” Mr. Williams said, singing into the phone in an interview.

“She said, ‘Can you do anything with that?’” he added. “I said, ‘That’s your love theme.’”

Yet a poignant scene of her playing “Evergreen” on the guitar was cut from the movie.

On Friday, Netflix is bringing this version of the Grammy-winning song to light with an edition of the movie featuring never-before-seen original footage — the addition of which Ms. Streisand managed, the streaming service said.