Bayern were a threat every time they had the ball, however, and their second arrived shortly after the interval when Gokhan Gonul turned into the back of his own net from close range.
Besiktas - the first Turkish side to win a Champions League group - fielded six players aged 30 or older.
English referee Michael Oliver had to "paws" the game to shoo the animal away from the pitch, with Bayern quickly making fun of the moment on social media. - Jupp Heynckes is the first manager in Champions League history to win 11 consecutive games.
But that was as good as it got for the hosts and Wagner chested in Alaba's deflected cross six minutes before the end after Bayern found too much space down the right side of Besiktas' defence.More news: Sessions to fire FBI's McCabe before he retires?
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Bayern posted a photo-shopped image of Wagner with the cat posing on his shoulder before including the feline in a man-of-the-match poll.
The quarter-final draw will take place on Friday.
"Besiktas hadn't lost here in the Champions League, so it wasn't easy".
Nevertheless, Lewandowski played until the 67th minute, but failed to add to his 32 goals this season in all competitions.
Bayern has won its last two games-against Freiburg and Hamburg-by a combined score of 10-0.