Anthony Nwakaeme drew first blood for Trabzonspor in the 26th minute at Medical Park Stadium in Trabzon.
Veteran midfielder Marek Hamsik made it 2-0 for The Black Sea Storms in the 54th minute at home.
Trabzonspor is on an eight-game win streak and have not lost a match in 27 games in Turkish Super Lig.
The team is atop the Super Lig table with 39 points while Adana Demirspor is in the 10th spot with 20 points.
Galatasaray settle for 1 point at home
Galatasaray drew with Altay 2-2 at home Saturday.
Altay scored first in the 17th minute with Cesar Pinares at NEF Stadium in Istanbul.
Halil Dervisoglu equalized in the 34th minute, ending the goals in the first half.
Mbaye Diagne gave The Lions hope in the 79th minute when he scored but Daouda Bamba dashed dreams of a victory in the 86th minute as he scored on a penalty kick.
The Lions have not had a win in their last four matches in the Super Lig.
Galatasaray is sixth in Turkish Super Lig with 23 points, 16 points behind Trabzonspor.
Altay is in the 13th position with 18 points.
SATURDAY'S RESULTS:
Alanyaspor-Sivasspor: 0-1
Trabzonspor-Adana Demirspor: 2-0
Galatasaray-Altay: 2-2