Despite losing Jerome Boateng to a red card early in the second half, Jupp Heynckes' men cruised to a victory that ensured they finished on top of the pile in Group F
Goal from Mario Gomez, Thomas Muller, Xherdan Shaqiri and David Alaba gave the Bavarians revenge for their defeat in Belarus in October, despite Jerome Boateng seeing red just five minutes into the second half.
Bayern began the game in complete control and could have been ahead before their opponents had even had a kick, but Bastian Schweinsteiger scuffed his shot from the edge of box safely into the hands of Andrey Gorbunov in the BATE goal.
The visitors defended deep and pressed whenever Die Roten approached the final third, looking to catch the Germans on the counterattack or from a set piece.
Indeed, they might well have taken an early lead when their first real period of passing ended with Artyom Kontsevoi striking across goal from 20 yards, but his shot lacked sufficient power to truly trouble Manuel Neuer.
Having already secured qualification and aware that a win of any kind would see them top Group F, the hosts perhaps looked a little too relaxed in the opening 20 minutes, but took the lead when Shaqiri shifted up a gear. The Switzerland international was fortunate to evade Denis Polyakov’s challenge on the left, but did superbly to pick out Gomez for a tap-in after having made it to the byeline.
Toni Kroos sparkled only intermittently but almost doubled the Bavarians’ five minutes before the break, turning to strike a fierce shot from the edge of the box that was well stopped by Gorbunov.
BATE, too, played largely in second gear, with their route to the Europa League already sealed, and the game look like picking up until five minutes into the second half when Boateng was shown a straight red card for needless two-footed tackle on Rodionov.
However, just as it looked like the visitors were going to show more ambition and really take the game to the 10 men, a deep free kick was flicked on by Schweinsteiger for Muller to cushion his volley past Gorbunov from a matter of yards out - though most probably from an offside position.
Shaqiri then made it three shortly after the hour mark, heading home from six yards after a fine cross from Gomez on the left.
Polyakov’s miserable night was complete with 20 minutes remaining when he was dismissed following a second booking for simulation, after a ludicrous attempt to win a penalty for his side.
Alaba rounded off the scoring with his first ever Champions League goal, controlling well before coolly volleying fellow substitute Franck Ribery’s corner past Gorbunov from 18 yards out.
Egor Filippenko then tucked his neat finish inside Neuer’s post from the edge of the box with two minutes remaining, but it was nothing more than a consolation.
The victory ensured Bayern ended the group stage on a high with their 16th victory in their last 17 home Champions League ties.