It took the Bavarians 69 minutes to get going at the Allianz Arena but Thomas Muller, Xherdan Shaqiri and Luiz Gustavo then struck to give them another win and take them on to a record 88 points for the season.
Shortly after the final whistle, Bayern picked up their first trophy in three years before setting off on a parade from the stadium to the city centre, where 20,000 fans were expected to greet them on the balcony of the City Hall.
Coach Jupp Heynckes picked his strongest team for this Bavarian battle having rested several of his players for the draw with Borussia Dortmund a week ago.
They nearly opened the scoring in the sixth minute when Muller headed Arjen Robben's cross goalwards, but a fine save from Alexander Manninger managed to turn the ball past the post.
Augsburg, desperately in need of points to avoid relegation, responded and Tobias Werner tested Manuel Neuer for the first time in the 15th minute.
Soon after, Mario Mandzukic wasted an even better opportunity when he shot straight at Manninger from Franck Ribery's cross.
Manninger was kept busy as the Champions League finalists searched for a way through, but Ji Dong-Won was ensuring the Bavarian minnows had chances of their own.
Bayern eventually broke Augsburg's resistance in the 69th minute when Dante sent the ball into the six-yard box for Muller, who headed in with no Augsburg defender picking him up.
The goal opened Augsburg up and Shaqiri added a second in the 82nd minute when he linked up with Ribery before beating Manninger.
And Gustavo completed the scoring in the 88th minute with Ribery once again the provider.
There was no need for any stoppage time as the celebrations commenced punctually after Bayern's 28th win of the season.
Augsburg, meanwhile, go into their final game of the season still level on points with 15th-placed Fortuna Dusseldorf.