The struggling hosts extended their own unbeaten streak to three games to move out of the bottom three as they prevented Dortmund from setting a new club record of nine wins in a row.
Dortmund's lead at the top of the Bundesliga is therefore reduced to five points after second-placed Bayern won 7-1 against Hoffenheim.
Augsburg showed no fear against a side who had won their last eight games in a row and had not been beaten in the Bundesliga since last September.
They had the first chance of the game in the 13th minute when Roman Weidenfeller had to dive to keep out Torsten Oehrl's header.
Dortmund almost inflicted damage on themselves 10 minutes later when Sven Bender's clearance hit Mats Hummels and the ball ricocheted just wide of the post.
The league leaders threatened for the first time in the 40th minute when Robert Lewandowski's header was cleared off the line by Sebastian Langkamp, but it was a rare example of why Jurgen Klopp's side are favourites to defend their title.
Dortmund captain Sebastian Kehl was fortunate not to be shown a second yellow card when he voluntarily took a tumble inside the Augsburg penalty area in the 56th minute.
Four minutes later, Simon Jentzsch made a world-class save to keep his side level as he got his fingertips to Kevin Grosskreutz's header to push the ball wide of the post at full stretch.
It was the closest Dortmund came all evening to scoring as they were unable to respond to Bayern's emphatic success earlier today.