While Galatasaray can boast of four successive Champions League appearances, their performance in the 2014/2015 edition was an embarrassment, taking just a single point from the group stage.
Galatasaray also had a Spanish opponent in their group two years ago, struggling to 4-1 and 6-1 defeats to Real Madrid, while Atletico thrashed Besiktas when they took on the Turkish side in the quarter-finals of the Europa League in 2012.
French global Griezmann stunned the traditionally boisterous Istanbul crowd into silence with a goal in the 18th minute, slamming the ball past Fernando Muslera after finding himself unmarked in the box.
Atletico coach Diego Simeone had demanded a strong start to the competition after his team fell 3-2 at Olympiacos in last season’s group opener.
Juanfran’s cross found Griezmann in the area and the Frenchman struck a diagonal shot past a helpless Muslera.
Koke crossed towards the far post where Godin knocked it back for Griezmann who was perfectly placed to send the ball flying into the back of the net from close range.
Galatasaray reacted and Wesley Sneijder’s hard drive from 25 yards was kept out by Oblak.
Galatasaray have a fantastic squad similar to Atletico Madrid in a way and both play attacking passing football.
First-half substitute Umut Bulut did provide a spark for Gala, with the 32-year-old going close either side of the interval.
But Atletico could have even have grabbed a third just before the break, with Muslera saving a powerful header from Jose Gimenez.
Sneijder missed another chance when he drilled a long-range attempt off target.
After half time, the Turkish side’s ex-Arsenal forward Lukas Podolski horribly miscued a delicate cross from Denayer, burying his head in his hands in shame.