Bayern entered Turkey with a commanding 5-0 advantage after a dominant performance against a 10-man Besiktas in Munich last month, and the excellent Thiago Alcantara wasted little time in adding a sixth on the day.
Sandro Wagner wrapped up a comfortable win for Bayern with a tap-in.
Besiktas are unbeaten in their last six Champions League home games, though five of these have ended as draws (W1).
They did manage to pull a goal back through Vagner Love's effort in the 58th minute which breathed some brief life into the hosts and the 40,000 home fans.
But Muller created a fine goal for Thiago to get Bayern up and running, the midfielder timing his run into the box perfectly to tuck away a first-time finish from a pinpoint right-wing cross.
Though Bayern continued to cruise through the game, going closer to the second goal when Hummels headed wide from an Alaba corner, there was some concern for the German champions when goalscorer Thiago was forced off with injury to be replaced by James Rodriguez 35 minutes in.
An innocuous right-wing cross from Rafinha should have been easy to clear, but Gonul poked the ball past Zengin under no pressure whatsoever.
But Bayern scored their third of the night with six minutes remaining when substitute Wagner chested a deflected cross into an empty net.