Cim Boms victory gives it the maximum six points from the first two rounds, goal difference putting it ahead of Ankaragucu and Besiktas, the only other sides with a perfect start to the season.
The Ankara side beat Denizlispor 3-2 and the Black and White Eagles scrapped a 2-1 away win over newly promoted Kasimpasaspor.
Reigning champion Fenerbahce finally got on the board, defeating visiting Gaziantespor 2-1 on Saturday, making up for its humbling loss against league newcomer Istanbul Buyuk Belediyespor in the opening round.
In round twos other games, Konyaspor and Kayserispor drew one all, Manisaspor beat Ankaraspor 2-1, Rizespor went down at home 0-2 against Genclerbirligi, Sivasspor topped Istanbul BB by two goals to one, and OFTAS lost two nil against Trabzonspor.
After two rounds, Galatasaray leads on six points, followed by Ankaragucu and Besiktas with the same tally. The comes, Kayserispor with four points, Trabzonspor, Gaziantepspor, Istanbul BB, Sivasspor, Manisaspor, Fenerbahce and OFTAS all with three.
Denizlispor, Konyaspor and Bursaspor all have one point from their two outings, with Ankaraspor, Kasimpasaspor and Rizespor yet to open their account.