The French club have been giant killers in the Top 14 and an Augustin Figuerola try ensured they claimed their first European win before Nick Macleod snatched a losing bonus point with a last-minute drop goal.
Benjamin Urdapilleta booted Oyonnax into the lead after just three minutes at Stade Charles Mathon but Sale grabbed the first try.
As the 15-minute mark approached the ball was spread to Rob Miller, who threaded a pinpoint kick through for Phil MacKenzie, who collected the ball and stepped inside Silvere Tian to score.
Macleod added the extras but Urdapilleta quickly hit back as Oyonnax responded in perfect fashion.
They took the lead on 22 minutes as Figuerola caught the Sharks napping with a quick tap on the edge of the 22 to dart over.
Urdapilleta was once again on target and the French club weathered a Sale storm to enter the break leading 13-7
A stalemate then ensued in the second half until Nicolas Vuillemin struck a penalty on the 74th minute and Macleod responded.