First recorded by Harold Melvin & The Blue Notes (UK #5 1975).
Hit versions by Thelma Houston (US #1/R&B #1/UK #13 1977), The Communards (US #40/UK #1 1986).
http://youtu.be/zdU9rAJFs6I
From the wiki: “First charting as a hit for Harold Melvin & the Blue Notes, an act on Gamble & Huff’s Philadelphia International label, in 1975, ‘Don’t Leave Me This Way’ was later a hit single for both Thelma Houston and The Communards. The Blue Notes’ original version of the song featured Teddy Pendergrass’ lead vocal, and was included as an album track on the group’s successful Wake Up Everybody LP but the recording was not released as a single in the US.