Mesut Ozil converted the penalty successfully in the 14th minute to score opener for Fenerbahce at Istanbul's Ulker Stadium.
However, Besiktas responded quickly after Josef de Souza fired the right footed shot in the box to the far post in the 25th minute.
Five minutes later, Mergim Berisha gave Fenerbahce a lead again and the first half ended 2-1.
In the second half, Josef de Souza scored the equalizer with a powerful header, assisted by Ridvan Yilmaz with a cross in the 59th minute.
Both sides couldn't break the tie in the rest of match that ended 2-2.
Fenerbahce are now in the fifth spot with 28 points, while Besiktas collected 25 points in 17 matches to sit in the ninth place.
