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Four minutes later Marco Reus gave the German champions the lead with a direct free kick from a narrow angle.
However, Augsburg almost equalised immediately as Matthias Ostrzolek saw his attempt on the Dortmund goal saved by Weidenfeller.
The visiting goalkeeper was called into action soon after, this time Daniel Baier firing at him from 25 yards.
Torsten Oehrl was set up by Werner with a cross in the 17th minute, but his effort went harmlessly over the crossbar.
Oehrl came close again for Augsburg with a half-volley from the edge of the area, and then just before half-time Baier was denied by Weidenfeller.
All those missed chances could have come back to haunt the hosts moments later had Mario Gotze's powerful shot not rattled the post.
Then with 20 minutes remaining on the clock, Lewandoswki and Gotze combined in an attacking move that the former eventually finished for his second goal of the afternoon.
Sascha Molders notched up a consolation goal for Augsburg in the 81st minute when he headed home Ostrzolek's cross.