Peter Stoger's team have been coping without the firepower of Pierre-Emerick Aubameyang following his January move to Arsenal, largely thanks to Michy Batshuayi, and they have also been boosted by the return of Marco Reus.
The German international made a quick impact on Monday evening as he nudged the home side ahead by winning a one-on-one challenge with the goalkeeper in the 16th minute at the Westfalenstadion.
The home side were relatively comfortable in the first half, but they suffered a moment of nerves towards the half-time whistle when Augsburg won a free kick on the edge of the box.
After the half-time break, Andre Schurrle came close to doubling Dortmund's lead by latching on to the ball in the box, but his effort dragged wide of the left post.
Four minutes later, the hosts were punished for not taking their chances as Kevin Danso received the ball from a corner kick and managed to smash it into the roof of the net.
In the end, the visiting side were able to hold on to a point, which has moved the club up to eighth in the Bundesliga, while Dortmund remain second.
DORTMUND (4-2-3-1): Burki; Schmelzer, Toprak, Sokratis, Piszczek; Castro (Dahoud 62'), Weigl; Schurrle, Gotze, Reus (Pulisic 77'); Batshuayi
AUGSBURG (4-2-3-1): Hitz; Max, Hinteregger, Danso, Framberger (Heller 56'); Khedira, Moravek (Parker 77'); Caiuby (Kacar 92'), Koo, Schmid; Gregoritsch