The 24-year-old scored twice within the space of six minutes to hand the visitors an early lead in a first half that produced four goals.
Owusu grabs his first on 12 minutes before adding a second in the 18th minute, but Damac halves the deficit through Emilio Zelaya in the 25th minute.
However, ten minutes to half time Al-Ahli restored their two-goal lead Ljubomir Fejsa.
Owusu did not return after the break with what looked like he picked a knock, and his absence was greatly felt as Ahli failed to produce an attacking threat in the second half.
Emilio Zelaya netted his second with 15 minutes left to reduce the deficit before Farouk Chafai levelled a minute later.
Mazen Abu Shararah then grabbed the winner for Damac in injury time.
Samuel Owusu has now scored three goals in five games for Al-Ahli since joining on loan in the summer from Al-Fayha. Read Full Story