Fousseni Diabate broke the deadlock in the eighth minute for the home side but Galatasaray came back from 1-0 down with Akturkoglu's two goals in the first half.
Akturkoglu, 22, converted a penalty in the 64th minute to complete his hat-trick as his impressive performance led Galatasaray to seal a comeback win at the Gursel Aksel Stadium in Izmir.
Galatasaray are now in third place with 65 points, six points behind the leaders Besiktas, with seven games remaining of Super Lig.
