Elliman's singing career began in the early 1970s in London where she performed as a vocalist at various bars and clubs. This led to a recording contract and a close association as a backing vocalist for Eric Clapton. She performed on many of his 1970s hits including "I Shot the Sheriff".

She sang the role of Mary Magdalene in the original album of Jesus Christ Superstar and in the subsequent Broadway and film versions, and achieved her first hit single with the ballad "I Don't Know How to Love Him". The song was her first entry on the U.S. charts, peaking at #28 pop in 1971, although a cover version by Helen Reddy was a bigger hit. This performance led to a 1974 Golden Globe nomination for Best Actress in a Musical or Comedy.

Her recording career began to take off from this point and she scored several hit singles throughout the world, including cover versions of the Barbara Lewis hit "Hello Stranger" (which topped the Adult Contemporary charts for four weeks) and the Bee Gees' "Love Me". Her biggest success came in 1977 with her #1 hit from the Saturday Night Fever soundtrack, "If I Can't Have You" which was also written by the Bee Gees. The huge success of the latter song has resulted in Elliman being remembered as a disco artist, though this style of music was an exception to the medium-tempo ballads that she specialized in, and which comprised the bulk of her recordings.

A few minor Top 40 hits followed in 1979, including the title theme song from the film Moment by Moment and another disco track "Love Pains" which was a major club success. The single "Savannah" was also a minor hit and demonstrated Elliman's attempts to move away from disco music and create music that focussed more on her vocal abilities. During this time Elliman married and shortly thereafter decided to leave her career and spend time raising her family.

An album titled Simple Needs, with all songs written by Elliman, was released in 2004.