Kouka opened the scoring in the 21st minute after meeting Ivan Cavaleiro's cross with a fine volley from a tight angle.
He was replaced on three minutes past the hour mark while his side were leading 2-1, making way for Angolan striker Wilson Eduardo.
This goal is the fifth for the Egyptian international in the Turkish league and the sixth in 14 appearances in all competitions.
Alanyaspor lie ninth in the league table with 21points from 16 games.
Kouka spent last season on loan at Turkish side Konyaspor, where he scored 11 goals in 38 appearances on all fronts.
He returned to Olympiacos last summer and made just two appearances with the Greek club before moving to Alanyaspor.
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