Galatasary's poor disciplinary record continued in Austria and helped Sturm Graz to recover from their horrendous showing in Glasgow last week.
This ill-tempered game saw Suat Kaya red carded in the 69th minute but by then Sturm were well on the way to victory.
Iranian international Mehrdad Minavand created the first goal in the 31st minute when his drive was deflected into the path of Sergei Yuran to poke the ball home.
Minavand set up the second when he crossed for Markus Schopp to flick the ball home and his namesake Markus Schupp chipped the ball over Brazilian goalkeeper Taffarel eight minutes from the end to beat Gala with a showing that was unrecognisable from their fear-filled performance in Glasgow last week.
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