He suffered the first hairline fracture in his left foot in March a year ago and then broke two bones in it during the Champions League quarter-final at Real Madrid the following month.
Sandro Wagner wrapped up a comfortable win for Bayern with a tap-in.
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.
The quarter-final draw will take place on Friday.
It was a record 11th straight victory in the competition for coach Jupp Heynckes, who had led Bayern to the title in 2013 before retiring and returning this season.
"Besiktas hadn't lost here in the Champions League, so it wasn't easy". - The last time Bayern won at least six consecutive games in a single European campaign was back in the 1995-96 UEFA Cup, when they won seven on the bounce on the way to lifting the trophy.
Nevertheless, Lewandowski played until the 67th minute, but failed to add to his 32 goals this season in all competitions.