In minute 32, the Black Eagles' Turkish forward Guven Yalcin scored a fantastic right-footed volley in Istanbul's Vodafone Park, following his teammate Valentin Rosier's cross from the byline.
Sivasspor goalkeeper Muammer Yildirim did not move.
Near the end of the first half, Besiktas manager Sergen Yalcin was shown a red card for his reaction.
Besiktas' Can Bozdogan fell after a Sivasspor player's tackle. He seemed injured but the referee said play on. Another Besiktas player Serdar Saatci wanted to send the ball into touch for his teammate's treatment. But Sergen Yalcin rushed from his bench to kick the ball towards the pitch, reacting to the referee's decision, and he was immediately sent off.
In the 54th minute, Besiktas left-back Ridvan Yilmaz scored an own goal with a header, chipping the ball over goalie Ersin Destanoglu.
Guven Yalcin scored the winning goal for Besiktas with a header in the area in the 69th minute.
Yilmaz whipped the cross from the left flank to assist him.
Sivasspor have taken risks for an equalizer but the visitors' Pedro Henrique wasted a clear chance.
In minute 82, Sivasspor winger Max Gradel crossed the ball for forward Mustapha Yatabare, who was in the Besiktas area.
Yatabare nodded the ball to Pedro Henrique, but the Brazilian, who was unmarked, missed a close-range half volley.
Besiktas won the match 2-1.
The victors Besiktas are in the second position in the league, with 17 points in eight matches.
Sivasspor are in the 12th spot with nine points.
Trabzonspor top Super Lig
Trabzonspor won against Yukatel Kayserispor 2-1 to be on top of the league.
Greek midfielder Anastasios Bakasetas netted two goals, including a penalty, for his team to bring a win.
Emrah Bassan was the scorer for Kayserispor in the match.
The club from the Black Sea region have 18 points to top the division.
Results:
VavaCars Fatih Karagumruk - Medipol Basaksehir: 3-1
Fraport TAV Antalyaspor - Adana Demirspor: 1-2
Ittifak Holding Konyaspor - Aytemiz Alanyaspor: 1-1
Yukatel Kayserispor - Trabzonspor: 1-2
Goztepe - GZT Giresunspor: 0-1
Besiktas - Demir Grup Sivasspor: 2-1
