BATE never threatened a repeat of their 3-1 upset earlier in the competition as a much-changed Bayern side did more than enough to ensure they will avoid the likes of Barcelona and Manchester United in the next round.
Mario Gomez, one of seven changes, opened the scoring on 21 minutes and while Jerome Boateng saw red soon after half-time, Thomas Muller and Xherdan Shaqiri quickly netted to ensure a nerveless second period.
BATE were also reduced to 10 men on 69 minutes when Denis Polyakov was given a second caution, before substitute David Alaba completed the rout on 83 minutes. Egor Filipenko grabbed a BATE consolation a minute from the end.
Shaqiri and Gomez combined for the opener. The Switzerland international wriggled his way down the left to the byline and fired in a low pass that Gomez only had to turn in with an outstretched leg.
Bayern spent the remainder of the half threatening a second goal without finding it.
The task looked tougher when Boateng was sent off five minutes after the restart for a bad challenge on Artem Kontsevoy, but Muller and Shaqiri soon got themselves on the scoresheet.
Muller's goal came from an innocuous Kroos long free-kick that Schweinsteiger flicked on for his Germany colleague to turn in from six yards.
Shaqiri made it 3-0 on 65 minutes with a strong header, holding off the attention of a defender behind him, to steer Gomez's left-wing cross past Gorbunov.
Bayern were in full control and, when Polyakov was also sent off, a fourth goal arrived when Alaba volleyed home a Franck Ribery corner in the closing stages.
BATE at least signed off their Champions League campaign with Filipenko's late 18-yarder as they prepare for the Europa League.
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