Greece striker Gekas took his tally for the season to six with a fine brace, the first coming in the 23rd minute as he converted Bilal Kisa's ball over the top with a vicious half-volley.
The 34-year-old then added a second in the 49th minute to give the hosts all three points, Fener goalkeeper Mert Gunok unable to keep out his effort despite getting a hand to the shot after Gekas had collected a clever pull-back from Bruno Mezenga.
Victory for Akhisar sees them move to the top of the early Super Lig standings on 10 points from their first four games, two ahead of Besiktas after Slaven Bilic's men were held to a 1-1 draw by Eskisehirspor.
Midfielder Olcay Sahan put Besiktas ahead after 21 minutes but defender Berkay Dabanli levelled in the 72nd minute for the visitors, who clung on for a point despite attacker Rogelio Funes' dismissal four minutes from time.
Galatasaray bounced back from their surprise defeat to Balikesirspor last time out with a 2-1 success against Sivasspor, goals from Aurelien Chedjou and Burak Yilmaz proving enough for Cesare Prandelli's men.
A double from midfielder Berat Tosun ensured that Balikesirspor did not repeat their heroics as the newly promoted side were brought back down to earth with a 3-1 loss at Genclerbirligi.
Rizespor's poor start to the season continued with a 1-0 home reverse versus Bursapor, while Trabzonspor are still waiting for a first win after a 1-1 draw by Kasimpasa, a result that marked their fourth straight league stalemate.
Forward Yusuf Erdogan looked to ensured triumph for Vahid Halilhodzic's side with a 15th minute strike, only for Ezequiel Scarione to dash those hopes by hitting home in the 85th minute.
Elsewhere, bottom club Karabukspor lost 2-0 at home to Mersin Idmanyurdu, Konyaspor drew 1-1 with Kayseri Erciyesspor and the game between Gaziantepspor and Istanbul Basaksehir finished goalless.
