"Sleep Like Breathing" is a song by British singer-songwriter Alison Moyet, released in 1987 as the fourth and final single from her second studio album Raindancing. A duet with David Freeman, "Sleep Like Breathing" was written by Freeman and Joseph Hughes, both of whom made up The Lover Speaks. The song was produced by Jimmy Iovine, Freeman and Hughes.

During recording sessions of Raindancing, The Lover Speaks contributed three songs to the project, although only "Sleep Like Breathing" was included on the album. Upon release, "Sleep Like Breathing" failed to reach the UK Top 40. It peaked at No. 80 and remained in the Top 100 for three weeks. A promotional video was filmed to promote the single, which also featured Freeman.

The single was released by CBS on 7" and 12" vinyl in the UK and Europe. The B-Side "Love Resurrection (Live)" was exclusive to the single. On the European 12" vinyl release, two additional live songs were included: "Ne Me Quitte Pas" and "Don't Burn Down the Bridge". In the UK, the 12" single featured only "Ne Me Quitte Pas" alongside "Love Resurrection" as the B-Sides. A limited edition 12" version was also issued in the UK, replacing "Ne Me Quitte Pas" with "Don't Burn Down the Bridge". The three live tracks were recorded at Wembley Arena on 13 May 1987.

Praising Moyet's "interpretive gifts" and Iovine's "understated production" on Raindancing, American magazine Musician described "Sleep Like Breathing" as being a track that has "such lasting allure". Jonathan Butler of People described the song as one of only two songs on Raindancing to "exhibit the haunting quality she [Moyet] is capable of". Butler described both "Sleep Like Breathing" and "Blow Wind Blow" as being "reminiscent of more cerebral, Kate Bush-like material."J. D. Considine of The Baltimore Sun said of the album: "...as such, there's nothing here as immediately winning as "Invisible" was, but plenty that sinks in after a few serious spins. "Sleep Like Breathing," for instance, allows Moyet to exploit her dramatic range to its fullest." Steve Hochman of Los Angeles Times said: "Moyet's voice needs - deserves - arrangements that either match its big, glorious and soaring quality, or offset it with spacious, atmospheric backing. While her second solo effort contains three gorgeous examples of the latter (including "Sleep Like Breathing"), it has none of the former."

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