Julian Green scored his first competitive goal for Bayern Munich as Carlo Ancelotti's side advanced to the third round of the DFB-Pokal with an ultimately comfortable 3-1 victory over Bavarian rivals Augsburg.

In the first of two meetings between the sides in the space of four days, promising youngster Green headed home 41 minutes into an eventful cup tie at the Allianz Arena, with Bayern having raced into an early lead courtesy of Philipp Lahm.

Augsburg had a chance to haul themselves back into the contest from the penalty spot early in the second half, but Manuel Neuer was in fine form to deny Koo Ja-cheol low to his left.

Thomas Muller should have put the result beyond doubt prior to the hour-mark, only for the German forward to blaze over from 12 yards out after Georg Teigl handled in Augsburg's area.

Ji Dong-won's terrific solo effort did apply some pressure on the hosts late on, but substitute David Alaba squeezed a thunderous strike past visiting goalkeeper Marwin Hitz in second-half stoppage time to ensure the defending champions went through.

Robert Lewandowski had to settle for a place on the bench, but Bayern did not miss the striker's influence as Lahm put them ahead within two minutes.

After sitting out the 2-0 win over Borussia Monchengladbach at the weekend, Lahm got his return to Ancelotti's line-up off to the ideal start when he fired home after combining excellently with Muller.

Bayern continued to dominate following the captain's strike, ambitious efforts from Muller and Thiago Alcantara respectively almost extending their advantage.

Thiago was dictating the Bundesliga champions' tempo as they continued to control proceedings, and he went close again when his deflected strike whistled wide.

But Bayern did double their tally four minutes before the interval, Muller again the provider as his cross found Green, whose header could not be kept out by Hitz.

Hitz atoned on the stroke of half-time, though, as he somehow kept out Mats Hummels' effort from point-blank range.

Augsburg should have pulled one back three minutes after the restart, Gojko Kacar winning a soft penalty after going down under pressure from Hummels.

However, Koo was unable to beat Neuer from the spot and Daniel Baier could only fire wide after reaching the rebound first.

Augsburg then found themselves on the opposite end of a penalty decision 12 minutes into the second half, but Muller fired over after referee Sascha Stegemann pointed to the spot for Teigl's blatant handball.

It looked like it could prove a costly miss in the 68th minute when Ji got the better of Jerome Boateng on the left-hand side of the box and thumped a stinging strike past Neuer.

However, the goal sparked Bayern back into life, Renato Sanches going close with a looping header before Thiago drilled narrowly wide.

Ancelotti's side made sure of their place in round three in the 93rd minute when Arturo Vidal played in fellow substitute Alaba, who hammered a venomous strike past Hitz to add gloss to the victory.