The Lions moved into first place following the win over the Anatolian Eagles.
Fenerbahçe are currently in second, one point behind Galatasaray following their 3-2 win over Sivasspor.
Third placed Beşiktaş will however, move into first place with a win against Gaziantepspor as they have a game in hand.
“I want to thank the boys, we did not play our best game but we got all three points, we will be champions,” Hamzaoğlu told Lig Tv.
Hamzaoğlu replaced former Italian national team manager Cesare Prandelli as Galatasaray head coach in November under current president Duygun Yarsuvat.
Galatasaray have won the league title 19 times as have rivals Fenerbahçe. The Lions will earn the right to wear a fourth star if they win the championship this season.
The Lions take on Mersin Idman Yurdu away from home next week in the league.