GFK were in poor form in the league, winless in their last four matches (two draws and two defeats).
It was a drab first half at the Gaziantep Stadium but the hosts came alive from the 67th minute, with Kayode heading the ball towards the path of Guray Vural, who finished the rest.
The Shakhtar Donestk loanee then made it 2-0 with a cool tap in six minutes later and finally sealed the victory from the penalty spot in the 90th minute.
Kayode's brace were his two shots on target in the entire duration of the game. He also had 24 touches and six accurate passes (60%).
The Nigerian forward's goal tally in the Super Lig now stands at five goals along with four assists.
Asides Kayode, with four Africans in Senegal's Papy Djilobodji, Cameroon international Jean-Armel Kana-Biyik and the Ghanaian duo of Patrick Twumasi and Raman Chibsah, all made the Gaziantep starting XI.
Twumasi was substituted in the 29th minute with a suspected injury, Kenan Ozer replacing him, while Chibsah was given a yellow card for a foul in just the fifth minute of action.
Marius Sumudica's side has moved up to 10th place on the log, and next come up against Kırklarelispor in the Turkish Cup on Wednesday.
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