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.
The German side went ahead through Thiago Alcantara in the 18th minute to kill off any lingering hopes of a miracle recovery by the Turkish team.
Bayern had crushed them 5-0 in the first leg in Munich.
The Spaniard, however, was taken off with a suspected ankle problem a little later after only recently returning from an injury break.
Bayern, who could secure their sixth consecutive Bundesliga title at the weekend, went 2-0 up seconds after the second-half restart when Gokhan Gonul volleyed a Rafinha cross into his own net.
Besiktas, who were missing their entire central defence, offered little resistance despite controlling possession.
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.
Yet Bayern substitute Sandro Wagner chested in a David Alaba cross with six minutes remaining to make sure of Bayern’s victory.
The quarter-final draw will take place on Friday.