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Pep Guardiola's side wasted little time in breaking the deadlock in the Bavarian derby, with Jerome Boateng volleying home on the turn five minutes in after waiting for Dante's flick to bounce at the far post.
Ribery fired over from distance soon after the opener following a mazy forward burst, with Augsburg restricted to looking for Andre Hahn with long diagonal passes.
Just before the break Ribery was brought down just outside the penalty area to give the hosts a dangerous free kick, which the Frenchman drilled into the top corner to extend Bayern's advantage.
The visitors finally succumbed to late pressure as Bayern added a third through substitute Thomas Muller, who tucked home a penalty just before stoppage time to add gloss to the scoreline.