Podolski then wasted a good chance for Germany when he was put clean through by Thomas Hitzlsperger, only for the Bayern Munich striker to blaze over with just Rustu to beat.
The second half was barely five minutes old when Olic came close again as he headed over Rustu and after sloppy defending had a second chance which was hacked off the line.
They had long periods of possession but, despite two good efforts from Gabriel Obertan, the hosts only came really close to equalising in stoppage time when they had a penalty shout before veteran Besiktas keeper Rustu made two superb saves.