The Belgian striker scored the opener with a close-range finish in the 12th minute at the Yeni Sivas 4 Eylul stadium.
Sivasspor leveled the match with a header from Mustapha Yatabare in the 26th minute, but Besiktas took the lead again with Rachid Ghezzal scoring in the 43rd minute.
The Black-Eagles were awarded a 73rd-minute penalty following a handball by Hakan Arslan, and Batshuayi converted the penalty kick.
In the 85th minute, Faycal Fajr narrowed the gap to one with a penalty goal, but it was not enough for the home side to win the game.
The Istanbul club are currently ranked fifth with 44 points, while Sivasspor are in the 12th spot with 34 points on matchday 27.
