Augsburg, the in-form team of recent weeks, started the match well against Bayern. They scored in the 30th minute to make it 1-0, but Musiala made it 1-1 in the 42nd minute. Augsburg could have taken a point from Bayern, but Zesiger received a red card in the 59th minute and Augsburg were reduced to 10 men. Just 1 minute later, Kane scored the goal that put Bayern ahead, into the Augsburg goal, and the score became 1-2. Matsima scored an own goal in the 90+3rd minute of the match, and the score ended 1-3 in Bayern's favor. With this victory, Bayern will start next week's match against Inter with high morale.
Yeah Augsburg has been an in form team in recent weeks, they have not lost any game on a while although they have had couple of draws which is why they haven't really moved up in the standings. They started well against Bayern Munich but they couldn't maintain the same momentum till the end. Bayern Munich turned the game around and took advantage to win the match with two goals up making it 1-3. It was an important victory for Bayern Munich else Bayer Leverkusen would have taken advantage of the situation if Munich had lost or drew as they will be closer to them and so the title challenge will be more intense.
Taking the games one game at a time will now see Munich prepare well for the champions league game with uplifted spirit just as you said.