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.
Despite needing victory to assure their place at the top of the group, Bayern boss Jupp Heynckes rang the changes from the team that drew 1-1 with Borussia Dortmund at the weekend.
That resulted in a completely changed back four with Daniel van Buyten, Jerome Boateng, Diego Contento and Rafinha handed starts
Anatoliy Tymoschuk came in to anchor the midfield alongside Bastian Schweinsteiger and it was the other two new men, Shaqiri and Gomez, who combined for the opener.
Gomez had already headed a Rafinha cross over but there was no missing after Shaqiri's penetrative run.
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.
Toni Kroos volleyed a 25-yarder over and a better effort soon after forced Andrey Gorbunov into a parried clearance.
Gomez flashed a shot wide before Denis Polyakov's well-hit effort from the edge of the area was just off target to provide a reminder the hosts still had work to do.
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, which promisingly began with back-to-back wins, with Filipenko's late 18-yarder as they prepare for the Europa League.