Jurgen Klopp's men ended their last league outing in a disappointing 0-0 stalemate at home to Stuttgart, but there were no signs of such a result repeating itself as the visitors strolled to a comfortable victory to see their fleeting title defence endure for another week.
Marco Reus opened the scoring with a free-kick right out of the top drawer, before a Robert Lewandowski double in the second half put Dortmund in cruise control.
Sascha Molders pulled one back for the home side with nine minutes to go, but there was no time left for a further response, as Dortmund snatched all three points, but still remain 11 points behind league leaders Bayern Munich.
Klopp made two chances from the side that claimed a 2-2 draw against Real Madrid midweek, as Sven Bender replaced Sebastian Kehl, while Felipe Santana was handed a rare start ahead of Neven Subotic in defence.
Augsburg fashioned the first real opening of the game after only five minutes, when Tobias Werner forced Roman Weidenfeller to parry, and Lukasz Piszczek had to be alert to remove the danger from the rebound.
But four minutes later, Dortmund were ahead. Reus did not let the angle faze him as he took authority over a set-piece on the left side of the box, and curled a stupendous effort into the top corner that beat Simon Jentzsch all ends up.
Augsburg almost hit back straight from the restart, but Weidenfeller was alert once again to deny Matthias Ostrzolek, who had done well to get on the end of a dangerous cross.
Dortmund seemed unable to capitalize on their advantage, as they found it hard to assert themselves in the face of a determined effort from the home side.
Augsburg, for all their encouraging play, lacked a cutting edge up front, as shown succinctly in the 35th minute when the impressive Werner teed up Torsten Oehrl for a half-volley that ripped wide of the post.
However, with half-time looming, a pair of golden chances from either side nearly turned the game on its head.
First, Daniel Baier was left shaking his head after failing to convert from an unmarked position eight yards out, with Weidenfeller making the save, before Mario Gotze, with the last kick of the half, drilled onto the woodwork after a clever move involving Reus and Kevin Grosskreutz.
Gotze would be far more decisive six minutes after the interval, as he cushioned a long punt forward into the path of Lewandowski, who did enough to slot under the body of Jentzsch, and send the visitors into a two goal lead.
But Dortmund were lucky to see that advantage remain intact after the hour mark, as a furious attack by Augsburg saw Weidenfeller parry Andreas Ottl’s shot from close range, before Knowledge Musona ripped the rebound onto the base of the post.
With 20 minutes to go however, BVB put the result beyond any doubt. After a giveaway from Augsburg in their own half, Lewandowski played a give and go with Reus, profited from a missed clearance from Sebastian Langkamp, and buried past Jentzsch for the second time.
In the 81st minute, Molders finally gave the home fans something to cheer after turning home a delivery from Matthias Ostrzolek, but it was too little too late for Augsburg, who slumped to another defeat to remain rooted to the foot of the table.