Arjen Robben broke the deadlock on four minutes, rifling a volley into the net following a corner.
However, the winger's game was brought to an abrupt end just after the quarter-hour mark. He left the field in plenty of discomfort after being brought down by Augsburg goalkeeper Marvin Hitz.
Hitz received a yellow card, but a foul was not awarded because Robben had been called offside.
Bayern's lead rarely looked in danger and they doubled their advantage late in the second half, when Thomas Muller netted his fourth goal in five games.