The home side's Senegalese forward Mame Biram Diouf opened the scoring in the 21st minute at Antakya Ataturk Stadium.
Atakas Hatayspor doubled the lead when Portuguese midfielder Ruben Ribeiro made a classy long shot in the 29th minute.
Mame Biram Diouf netted twice to make the score 3-0 in the 72nd minute. In the 79th minute, Hataypor's Bulgarian defender Strahil Popov received a straight red card after he brought down Henry Onyekuru outside the penalty box.
Following this huge victory, sixth-place Atakas Hatayspor increased their points to 49 on the matchday 32.
Super Lig fixtures & results:
Saturday:
Hes Kablo Kayserispor - Goztepe: 1-0
Caykur Rizespor - Fatih Karagumruk: 0-0
Demir Grup Sivasspor - Trabzonspor: 0-0
Atakas Hatayspor - Galatasaray: 3-0
Sunday:
Buyuksehir Belediye Erzurumspor - Ittifak Holding Konyaspor
MKE Ankaragucu - Fraport TAV Antalyaspor
Medipol Basaksehir - Yeni Malatyaspor
Aytemiz Alanyaspor - Genclerbirligi
Kasimpasa - Besiktas
Monday:
Fenerbahce - Yukatel Denizlispor