Bayern were upstaged by rivals Dortmund in last season's semi-final but the Bundesliga champions exacted revenge on Wednesday with a 2-1 victory at the Allianz Arena.
Centre-back Jerome Boateng and Muller scored in the first half as Bayern moved into the fourth round.
Bayern have won 15 of their past 16 matches – and six in succession – since head coach Jupp Heynckes replaced Carlo Ancelotti in September
Speaking afterwards, Bayern forward Muller told reporters: "A little turbulence at Bayern Munich is exactly what the media wants. And winning 15 out of 16 games is something we look at with joy.
"That's why we are happy to play for Bayern, since you get never bored. The pressure is always there and in the past weeks we resisted that very well.
"We want to take this motivation into the second half of the season. We have a good base and we will continue to attack."
Muller, whose Bayern are not back in action until January 12, continued: "It was a nice ending to the year. We won against Dortmund now and already won against [RB] Leipzig as well.
"We look positively into the future and know that the break will help us. We invested a lot in the past month and I think it was visible that we were all happy that the match was finally over."
Heynckes was happy with the win but not completely satisfied after watching Bayern dominate in Munich without making their superiority count on the scoreboard.
"I think today we missed the chance to close the game. In other words – if we had used our chances in the first half, we would not have led the match 2-0 but 4 or 5-0," he said.
"We had huge scoring chances and dictated the game from the first to the last minute and played very fast because the opponent played with a triple chain that became a five-string. They played without a striker – that means without a centre forward. That's not all that easy then to play his game as we did in the first half."
"I think if I see the whole game – for an hour we dominated the game and with the scoring chances I also think that it was a highly deserved victory for my team," Heynckes added.