Emre Bassan opened the scoring for the visitors in the 22nd minute while Doka Madureira and Cikalleshi scored for Basaksehir in the second half.
The former Cameroon international striker scored twice in the 50th and 64th minutes earning his side three points.
Eto’o recently put pen-to-paper on a three-year deal with Antalyaspor earlier this summer. The 34-year-old has previously played for Sampdoria, Chelsea, Anzhi, Inter and Barcelona. Eto’o joined Sampdoria from Everton last season and scored six times while providing five assists in all competitions last season for the Serie A outfit
Antalyaspor were promoted to top-tier football at the end of last season but have embarked on an ambitious transfer policy. The Scorpions take on Genclerbirligi at home in their second game of the 2015-16 Turkish Super Lig season.