The substitute proved to be the difference in this Bundesliga clash, and despite a battling performance from the division's bottom side, they failed to get anything from the game
Goals from Thomas Muller and Mario Gomez wrapped up the win, which sees Jupp Heynckes' side stretch their lead to nine points ahead of second-placed Bayer Leverkusen who play Hannover on Sunday.
The home side caused early problems and inside the first five minutes, Dante was forced into making a goal-saving intervention, stopping Sascha Molders from tapping home a near post cross. Knowledge Musona then tested Manuel Neuer minutes later, but his well-struck effort was collected impressively by the German keeper.
After 24 minutes Bayern sprang into life, and Mario Mandzukic had Augsburg's Mohamed Amsif scrambling to his right, as the Croatian's scuffed strike trickled past the post. Seconds later, Franck Ribery whipped in a front post cross, but despite good movement from Mandzukic, the lone striker directed his effort straight at the opposition keeper.
In spite of their early resilience, Gibril Sankoh undid all of his side's work literally single-handledly on 39 minutes, handling the ball inside the penalty area, giving Bayern the chance to take the lead from the penalty spot. Thomas Muller coolly sent Amsif the wrong way, to convert his ninth goal of the Bundesliga season.
A minute before the break, Molders had a magnificent chance to level the scoreline, but the Augsburg forward headed way over the bar from a Tobias Werner cross, allowing Bayern a half-time lead.
The second half began similarly to the first, as Augsburg pushed on, but their pressing didn't come to any fruition, as Bayern appeared happy to let the home side retain the ball.
In the 61st minute, the misfiring Mandzukic was replaced by Gomez. The Germany international made an immediate impact, scoring two minutes later. After being slipped through on goal by Ribery, Gomez curled a great finish inside Amsif's front post to put Bayern firmly in control.
Attempting to salvage something from the game, Augsburg's unfortunate Sankoh was replaced by striker Stefan Hains on 72 minutes, as the relegation candidates pushed on in search of a goal.
However, Augsburg's gamble failed to pay off and with 15 minutes left to play, Bastian Schweinsteiger had to be denied brilliantly by Amsif. The Moroccan keeper threw out a strong right boot to divert the Bayern midfielder's goal-bound effort away from his net, which surely would have been the deciding goal.
The league leaders continued to push on, with little resistance or chances of note from the home side, as their first-half character escaped them for a large portion of the second 45 minutes.
Augsburg's frustrations were compounded by Aristide Bance and Hains miscommunication on the edge of the Bayern box, as neither striker were willing to let their team-mate drive the attack forward, ending up in a tangle of legs.
The clinical addition of Mario Gomez proved to be the vital change for the Munich side, as Mandzukic failed to put the game beyond Augsburg despite missing a catalogue of good chances.
The Bundesliga's bottom side put in a plucky performance, with the 2-0 scoreline somewhat flattering Bayern, as Markus Weinzierls' side extend their winless run to seven matches.