Born in Chicago, she grew up in a family she has described as "lower-middle-class-hillbilly-hipster" in Chicago, Los Angeles, Phoenix, Arizona, and Olympia, Washington. She settled in L.A. when she was nineteen, where she waited tables and played at local clubs. A 1979 contract with Warner Brothers Records resulted in her first, self-titled album. Commercially and critically well-received, it included a hit single, "Chuck E's in Love", and won her the Best New Artist Grammy award along with five other nominations.
She was featured twice in two years (1979-1980) on the cover of Rolling Stone magazine, and appeared four times as the musical guest on Saturday Night Live between 1979 and 1989. Since her debut, Jones has released several albums, none as successful as the first, though she won another Grammy (and two other nominations) for a cover of "Makin' Whoopee" with Dr. John.
Jones has one daughter from her marriage with French musician Pascal Nabet Meyer.