Noah, 20, and Billy Ray, 58, coordinated their performance via video during Wednesday's episode of the CBS late-night show.
Noah and her dad performed her song "Young & Sad." The recorded version of the song opens with a voicemail from Billy Ray that he left Noah during a "dark period" in her life.
"[It starts] with a voicemail my dad sent me a while ago during a dark period of my life reminding me to keep 'smiling' because at the time that he sent that, a smile seemed impossible for me to give," Noah told Rolling Stone in May.
Noah and Billy Ray also performed Noah's song "July."
"Young & Sad" and "July" both appear on Noah's EP The End of Everything, released in May. The mini album also features the singles "Lonely" and "I Got So High That I Saw Jesus."
In an interview with NPR in May, Noah said the title The End of Everything was inspired by John D. Boswell's documentary film Timelapse of the Future.
"It shows you the stars blinking out and the universe going dark, and Saturn's rings will one day disappear. And the universe will all one day come down to two black holes that'll dance together. And I started crying -- like, man," the star said.
"You know, my mom is my best friend. And I was, like, my time with her and my family is so limited. And that hit my heart so heavy," she added.
Noah is the daughter of Billy Ray and Trish Cyrus. She is the younger sister of singer Miley Cyrus.