Cameroonian forward Vincent Aboubakar scored from penalty in the 59th minute to break the deadlock at Vodafone Park.
In the 63rd minute, Besiktas doubled the lead. French winger Georges-Kevin N'Koudou scored on a quick counter attack. Besiktas' Croatian defender Domagoj Vida made it 3-0 for his team in 70th minute with a classy back-heel goal in the six-yard box.
Only a minute later Aboubakar finished in the penalty area to seal 4-0 win for Besiktas, their largest win of the season.
Besiktas increased their points to 22 to move to the fourth spot in standings.
Other title contenders Galatasaray and Fenerbahce had 23 points each to pursue the league leaders Aytemiz Alanyaspor, who bagged 26 points in 13 weeks.
Sunday's results:
Genclerbirligi - MKE Ankaragucu: 1-1
Yukatel Denizlispor - Aytemiz Alanyaspor: 1-0
Besiktas - Buyuksehir Belediye Erzurumspor: 4-0
