Besiktas - the first Turkish side to win a Champions League group - fielded six players aged 30 or older.
Jupp Heyneckes still plays a strong team, however, starting with Robert Lewandowski, Thomas Muller and Franck Ribery all starting.
David Alaba nearly opened the scoring for the Bavarians in the 11th minute with a free-kick that was parried away by Besiktas shot-stopper Tolga Zengin, while Thomas Muller could not turn home the rebound.
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.
However, Sandro Wagner bagged Bayern's third of the night six minutes before time after controlling Alaba's cross at the far post before firing home at the far post to seal a 3-1 win on the night and 8-1 on aggregate.
Comedian and 'Bullseye' Presenter Jim Bowen Dies Aged 80
On 27 August 2012, Jim reunited with co-presenter Sally Naden for a one-off show at BBC Radio Lancashire. Former BBC Radio Lancashire presenter and television host Jim Bowen has died at the age of 80.
Thiago limped off before half-time, giving Bayern an injury concern for the rest of the season. As Tolga attempted to punch clear a relatively innocuous Rafinha cross, the ball ricocheted off defender Gonul at point blank range and passed the hapless goalkeeper to give Bayern an extra boost they didn't really need.
Leipzig are winless in their last four league games and desperate to beat Bayern to boost their hopes of a Champions League place next season.
French striker Jean-Kevin Augustin says hosts RB Leipzig are determined to prevent Bayern Munich being confirmed as Bundesliga champions for the sixth straight year as early as this Sunday.
Last season, under Carlo Ancelotti, Bayern won the title with three games left.
Thiago Alcantara put Bayern 1-0 up in the 18th minute.