Neither team was able to break the deadlock in the first half at Vodafone Park.
Fenerbahce were reduced to 10 men in the 25th minute after Kosovar forward Vedat Muriqi was shown a red card with a video referee decision.
In the second half, Besiktas's Croatian defender Domagoj Vida scored the opener in the 63rd minute.
Turkish player Gokhan Gonul sent the ball into Fenerbahce's net in the 70th minute, making it 2-0.
Following this victory, the Black Eagles sit on the fourth place with 59 points while Fenerbahce are seventh in the division with 50 points.
Fenerbahce, with a week to go in the Turkish Super Lig, are failed to participate in European competitions.
