Netherlands international Wesley Sneijder fired Fatih Terim's side ahead within 10 minutes at the Turk Telekom Arena.
And it got better in the second half when Burak Yilmaz opened his account for the season from the penalty spot to effectively end the game as a contest.
Monday's other game saw Kayserispor record a 1-0 home win against Sivasspor.
Elsewhere, last season's league runners-up Fenerbahce suffered an opening-day shock as they surrendered a 2-0 lead to lose 3-2 away to Konyaspor on Saturday.
Joseph Yobo and an Emre Belozoglu penalty had given Ersun Yanal's side a two-goal cushion inside half an hour at the Konya Ataturk Spor Kompleksi.
Slaven Bilic's team had to be patient for victory with the away side showing stubborn resistance at the Recep Tayyip Erdogan Stadyumu.
Bursaspor are another side that harbour hopes of playing in Europe's elite competition, but their season started with a 2-0 defeat away to Eskisehirspor.
Akhisar Belediye were also victors on Sunday as they defeated Elazigspor 3-1, while Antalyaspor and Kayseri Erciyesspor played out a 0-0 draw on Friday.
