Nigeria international Paul Onuachu was the hero as his brace helped the team end a two-year run without silverware and also seal qualification for next season’s Europa League play-off round.
Fatih Tekke's Black Sea Storm made a strong start when Onuachu finished from close range in the 17th minute after a cross from Pina.
Konyaspor hit back early in the second half, with Jackson Muleka converting the rebound after his header struck the post ten minutes before the hour mark.
They had the chance to take the lead, but Enis Bardhi hit the post from the penalty spot in the 58th minute, before goalkeeper Andre Onana kept out Muleka’s follow-up effort.
Trabzonspor sealed the win in the 79th minute when they were awarded a penalty for handball, which their Nigerian import coverted to secure the trophy.