Dutchman Sneijder's two stunning late strikes gave Gala a 2-1 win over arch rivals and defending champions Fenerbahce on Saturday, yet it is Besiktas who continue to set the pace.
Slaven Bilic's men were given a scare by Sivasspor, though, with midfielder Olcay Sahan's 79th-minute strike finally settling an enthralling encounter.
Senegal striker Demba Ba opened his account in the league for Besiktas with a double that seemed to have sealed victory after Manuel da Costa had put visitors Sivasspor ahead.
Hakan Arslan levelled matters in the 74th minute, only for Sahan to pop up with a winner for the league leaders.
Away from Turkey's traditional big three, Akhisar Belediyespor returned to winning ways and moved third with a 2-0 triumph over Kasimpasa.
However, Mersin Idmanyurdu's strong start to life in the top flight ground to a halt with a 3-1 loss at Trabzonspor.
Defender Essaid Belkalem put Trabzonspor in front and Mersin then had Gokcek Vederson sent off after 57 minutes.
The 10 men levelled through Oktay Delibalta but their hopes of securing a share of the spoils were ended as Carl Medjani and Oscar Cardozo scored to seal maximum points for Vahid Halilhodzic's side.
Eskisehirspor earned a 2-2 draw at Bursaspor in dramatic fashion, two late goals in the space of five minutes securing a point after a double from striker Cedric Bakambu had seemingly put the hosts in command.
Rizespor and Balikesirspor drew 2-2 in a battle of two struggling sides, while elsewhere Gaziantepsor beat Karabukspor 1-0 and the games between Gengclerbirligi and Kayseri Erciyesspor and Konyaspor and Istanbul Basaksehir finished 0-0.