Galatasaray tested Champions League debutant Davy Roef in the early stages, but the young goalkeeper was equal to Felipe Melo's seventh-minute header.
At the other end, Fernando Muslera snaffled the ball off the feet of Yeori Tielemans.
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Matias Suarez arrived as a substitute midway through the half for the visitors and added impetus to their attack, with Ibrahima Conte, Aleksander Mitrovic and Olivier Deschacht all sending shots goalbound shortly after his introduction.
The home side struggled to cope with the energetic visitors, but Melo did see a goalbound strike deflected narrowly over the bar in the 34th minute.
Selcuk Inan then clipped the outside of the post with a free kick in the 40th minute as the hosts began to show signs that they were finding their way back into the game as the half-time whistle blew.