Demba Ba's penalty and full-back Daniel Opare's goal put Besiktas ahead but the visitor equalised on each occasion, Ermin Zec with the first and Ronald Vargas' 83rd-minute penalty earning them a point.
Besiktas had Pedro Franco sent off in stoppage time.
Istanbul Buyuksehir and Bursaspor continued their battle for fourth, and a place in the Europa League qualifying rounds, as both won.
Semih Senturk's penalty and Merter Yuce's own goal gave Buyuksehir a 2-0 win over Akhisar Belediye and kept it a point ahead of the Crocodiles, who beat Mersin Idmanyurdu 2-1 despite playing most of the game with 10 men.
Goalkeeper Harun Tekin was sent off in the 17th minute and his replacement Okan Kocuk was beaten by Milan Mitrovic's penalty, but Jose Fernandao equalised - also from the spot - and Renato Civelli scored the winner.
Kasimpasa also won with 10 men, 2-1 against Gaziantepspor.
Ezequiel Scarione got the opener and though Orhan Sam was sent off early in the second half, Andre Castro scored the second four minutes from time.