The Human singer was recording new house music tune I Can Change, which samples Bronski Beat's 1980s hit Smalltown Boy, when he decided the tune lacked a certain voice.
Flowers texted Tennant a line and asked him to call up and leave it on his cellphone answering service.
The Killers star says, "We just had this gap in a verse and we needed to stick something in there. We were talking about it being a speaking part, and the greatest musical 'speaker' is Neil Tennant! His voice is like no other.
"He didn't even hear the song or the tempo or anything. I just texted him this line. I asked, 'Will you send us a voicemail of yourself saying, 'When you're looking for a change'? And that was it. He sent us a voice memo, and we stuck it onto the track, from the phone. It was done within 20 seconds."
The finished track features on Flowers' upcoming solo album The Desired Effect.