Batshuayi scored from the penalty spot in the 39th minute at Ataturk Olympic Stadium after Fatih Karagumruk left-back Caner Erkin's handball in the area.
Following their matchday 22 win, Besiktas boosted their points to 35 to be in third position in the Super Lig.
The Black Eagles are seven points behind second-place Ittifak Holding Konyaspor, who beat Adana Demirspor 1-0 at home.
Trabzonspor are obviously comfortable on top of the division as the Black Sea club bagged 50 points in 21 matches.
Mid-table Fatih Karagumruk have 30 points.
