Neither team was able to break deadlock in the first half at Istanbul's Vodafone Park stadium.
In minute 58, Galatasaray were down to 10 men as Senegalese forward Mbaye Diagne was shown a red card for fouling Besiktas' Francisco Montero.
Josef De Souza scored the opener from close range for Besiktas in the 79th minute.
In the stoppage time, Georges-Kevin N'Koudou doubled the lead as the game ended with a 2-0 score.
Besiktas remained at top of Super Lig with 38 points, while Galatasaray slipped to fourth place with 33 points.
Week 19 Fixtures & Results:
Friday:
Genclerbirligi vs. Fatih Karagumruk: 1-3
Saturday:
Konyaspor vs. Goztepe: 2-3
Basaksehir vs. Sivasspor: 1-1
Gaziantep FK vs. Kayserispor: 2-1
Antalyaspor vs. Trabzonspor: 1-1
Sunday:
Denizlispor vs. Hatayspor: 0-2
Yeni Malatyaspor - Caykur Rizespor: 4-1
Besiktas - Galatasaray: 2-0
Monday:
Kasimpasa - B.B. Erzurumspor
Fenerbahce - MKE Ankaragucu
