Joshua Kimmich starred for the hosts, scoring a brace. The other goals on the night were scored by Robert Lewandowski, Thomas Müller and Juan Bernat.
The win gives Carlo Ancelotti exactly what he would have expected before the game began and now Bayern go into their next games in fine form.
Lewandowski got the crucial breakthrough after initial frustration
The game started as expected with Bayern having plenty of the ball but they found it difficult to create any decent chances until they were awarded a penalty just before the half-hour mark.
The penalty was awarded when a corner was whipped into the box and Lewandowski was hauled to the floor and referee Anthony Taylor pointed to the penalty spot straight away much to the visitors disbelief. Lewandowski got up to take it and coolly slotted the ball into the net sending the goalkeeper the wrong way.
The home side stepped up the pace of the game after that and almost scored a second when Mats Hummels saw a flying header well saved by Soslan Dzhanayev, who had to make a high flying save to keep it out of the goal.
Müller scored the second just before half-time
The visitors looked like they were going to go in at half-time only the one goal down until Müller scored in injury time at the end of the half. A brilliant cross from David Alaba found the striker and all he had to do was the guide the ball home to double the lead.
It was literally the last kick of the first half which was harsh on the visitors as they had defended well for most of the half but class told at the crucial moment.
Kimmich scores a brace as Bernat rounded off a perfect night for the hosts
Just as it looked like Bayern had taken their foot off the pedal at the start of the second half and gave the visitors the chance to attack the hosts countered with pace to score a third goal. The goal was created this time by Douglas Costa, who produced a wonderful cross into the path of Kimmich, who slotted the ball into an empty net.
Lewandowski should have got his second goal of the game not long after when a cross from Costa found the striker unmarked at the back post but he put his shot over the bar when he should have scored.
The fourth goal though did come through Kimmich, who hadn't scored for Bayern before the weekend, got his second goal of the game when he headed in a cross like a true goalscorer.
After they scored the fourth, the hosts stepped off the gas and were intent on seeing out the game by keeping the ball. That was until the final minute of the game when Bernat smashed the ball home.
The full-back started the move off by running past a few players and played the ball to Frank Ribery who in turn cut the ball back to Bernat who made no mistake to round off a perfect night for Bayern.