However, Bayern striker Harry Kane scored in the 73rd minute and Jamal Musiala added another six minutes later to snap their opponents' 23-match unbeaten run across all competitions.
"It's my first time in this stadium and I'm just about getting my hearing back now," goalscorer Kane said.
"In the second half we were a bit more calm, better on the ball and took our chances.
Goalkeeper Sven Ulreich, however, had to come to the rescue only a minute later, spectacularly palming a Kerem Akturkoglu shot wide.
In an equally pacy start to the second half, the Turks had the lion's share of chances once more with Bayern defending desperately.
Persons:
Harry Kane, Jamal Musiala, Kane, Mauro Icardi, Kingsley, Sven Ulreich, Akturkoglu, Icardi, Ulreich, Karolos, Christian Radnedge
Organizations:
Bayern, Galatasaray, Champions League, Turks, Manchester United, Argentine, League, FC Copenhagen, Thomson
Locations:
ISTANBUL, Bayern Munich