Black Eagles broke the deadlock with an own goal from Babajide Akintola in the second minute at Istanbul's Vodafone Park.
Canadian winger Cyle Larin scored four goals in the 11th, 14th, 55th, and 65th minutes respectively, for the Black-Eagles.
Georges-Kevin N'Koudou and Ridvan Yılmaz also scored as Besiktas easily beat Atakas Hatayspor in the home game.
Besiktas are top of Super Lig to increase their points total to 81, with a home victory.
Having a game at hand, second-place Fenerbahce collected 73 points while Galatasaray have 72.
Besiktas will be crowned as Turkish Super Lig champions if they collect 4 points in the next three games.
Week 39 results & fixtures:
Besiktas - Atakas Hatayspor : 7-0
Yukatel Denizlispor - Caykur Rizespor
Ittifak Holding Konyaspor - Fatih Karagumruk
Fraport TAV Antalyaspor - Goztepe
Genclerbirligi - Galatasaray
Medipol Basaksehir - MKE Ankaragucu
Helenex Yeni Malatyaspor - Hes Kablo Kayserispor
Kasımpasa - Aytemiz Alanyaspor
Fenerbahce - B.B Erzurumspor
Gaziantep - Demir Grup Sivasspor</p>