Substitute James Hook booted a final kick conversion eight minutes into injury time to convert Wales star Shane Williams’ second try of the game.
Sale led 16-10 with the match in its final throes, but the Ospreys strung together numerous phases of attacking play before Williams scampered over.
Hook kept his nerve despite incredible pressure, leaving Sale facing a battle to reach the quarter-finals.
Sale could not build on Juan Martin Fernandez-Lobbe’s early try.
Fly-half Charlie Hodgson kicked three penalties and a conversion, yet only nine points were scored during an error-strewn second period before Williams and Hook took centre stage.
Tries: S. Williams 2. Cons: Connor, Hook. Pens: Connor.
Byrne, Walker, Parker, A. Bishop, S. Williams, Connor, Marshall, D. Jones, B. Williams, A. Jones, Cockbain, Evans, Tiatia, Tandy, R. Jones.
Hook for Connor (59), Spice for Marshall (57), James for D. Jones (60), Bennett for B. Williams (57), A. Jones for Cockbain (54), Thomas for Tiatia (57).
Tries: J. Fernandez Lobbe. Cons: Hodgson. Pens: Hodgson 3.
Robinson, Cueto, Taylor, Seveali’i, Ripol, Hodgson, Martens, Sheridan, Bruno, Evans, Jones, Schofield, White, Lund, J. Fernandez Lobbe. Replacements: Larrechea for Cueto (12), Wigglesworth for Martens (45), Briggs for Bruno (66), Turner for Evans (45), Chabal for Schofield (55).
J Jutge (France).