The 26-year-old replaced Mali defender Souleymane Diarra on the hour mark and got onto the scoresheet 19 minutes later.
Chibsah goal gave Gaziantep a three-zero lead after countryman Patrick Twumasi had opened the scoring in the 8th minute and Guray Vural after 58 minutes.
But Besiktas scored two goals in one minute to cause a nervy end to the match.
Another Ghanaian midfielder Abdul Aziz Tetteh lasted the entire duration for Gaziantep.
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