Hailing from the western province of Izmir, Goztepe got an early lead in the away game with Cherif Ndiaye's goal in the third minute at the Vodafone Arena.
Besiktas' Cyle Larin equalized the score in the 31th minute before the first half ended 1-1.
Rachid Ghezzal brought the lead to Besiktas in the 60th minute.
The Black Eagles finished the game with ten men as right back Valentin Rosier was shown a red card due to his second yellow in minute 81.
Besiktas is now placed seventh with 28 points in Super Lig standings, while Goztepe sits at 19th with 14.
Malatyaspor chair invades pitch after final whistle
After Yeni Malatyaspor drew with Kayserispor 2-2 at home in another Thursday Super Lig game, team chairman Adil Gevrek appeared to lose his temper, invading the pitch to argue with the referee Huseyin Gocek.
Goalie Ertac Ozbir grabbed Gevrek to calm him down.
After the incident at Yeni Malatya Stadium, Police surrounded the referees for protection before escorting them off the field.
Malatyaspor later tweeted a black screen in protest of the referee's decisions.
The club from eastern Turkey claimed that Gocek's decisions during the game were unfair.
Yeni Malatyaspor has yet to win a single match after eight games in the Super Lig, placing 18th in the table with 15 points, while Kayserispor is three spots above with 21 points.
Results:
Fraport TAV Antalyaspor-Kasimpasa: 1-1
Medipol Basaksehir-GZT Giresunspor: 3-1
Altay-Trabzonspor: 1-2
Adana Demirspor-Galatasaray: 2-0
Demir Grup Sivasspor-Caykur Rizespor: 1-1
Atakas Hatayspor-Ittifak Holding Konyaspor: 1-3
Gaziantep FK-Aytemiz Alanyaspor: 2-1
VavaCars Fatih Karagumruk-Fenerbahce: 1-1
Oznur Kablo Yeni Malatyaspor-Yukatel Kayserispor: 2-2
Besiktas-Goztepe: 2-1
