After finishing 12th last season, Akhisar have been in impressive form in the opening weeks of the campaign, with new head coach Mustafa Akcay guiding the team to seven points from three matches.
They fell behind to Cenk Ahmet's 33rd-minute opener in Kayseri, but Theofanis Gekas pulled the visitors level eight minutes after the interval.
It looked as though both sides would have to settle for a point, until Gekas struck again in the final minute to ensure Akcay's men returned home with all three points.
They are joined at the top on seven points by defending champions Fenerbahce, who were indebted to Emre Belozoglu's 82nd-minute penalty for their 1-0 home win over Gaziantepspor.
Besiktas also left it late to defeat Bursaspor 1-0 as they too moved to seven points after Olcay Sahan struck with four minutes remaining to earn them a maximum return.
Galatasaray's inconsistent start to the campaign continued as Cesare Prandelli's men went down 2-0 at Balikesirspor, who earned their first points of the 2014-15 season after first-half goals from former Gala man Sercan Yildirim and Gokhan Unal.
Prandelli's side have now taken four points from their opening three games and have already lost ground on traditional title rivals Fenerbahce and Besiktas.
At the foot of the early table, Karabukspor remain stuck on one point after a 2-1 loss at Kasimpasa, while Rizespor are only a point better off after they went down 2-0 at Mersin Idmanyurdu, for whom Servet Cetin and Sinan Kaloglu were the goalscorers.
Sivasspor complete the bottom three following their goalless draw with Konyaspor, while Trabzonspor needed an Oscar Cardozo equaliser in the third minute of stoppage time to earn a 1-1 draw at Istanbul Basaksehir.
Elsewhere, Genclerbirligi won 2-0 at Eskisehirspor courtesy of Ugur Ciftci and Bogdan Stancu.
