The Black Stars player lasted 75 minutes and was influential in the build-up to the game's only goal.
Greek midfielder Panagiotis Tachtsidis found Amadou Moutari, who blasted in the winner in the 73rd minute.
The win sends Al Fayha sixth on the league table as the chase for a top-four spot continues for the Oranges.
The 25-year-old has made 10 appearances this season and scored twice for the Pro League returnees.
Owusu has been named in Ghana coach Milovan Rajevac's squad for the final two matches of Group G in the World Cup qualifiers.
Ghana plays Ethiopia on November 11 before a final showdown with South Africa on November 14, 2021, in Cape Coast. Read Full Story
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