Jurgen Klopp's men were arguably the better side during the first half but still found themselves behind five minutes after the break when Raul Bobadilla pounced on a loose ball inside the area to slot home.
The visitors were reduced to 10 men 14 minutes later when Christoph Janker hauled down Pierre-Emerick Aubameyang with a professional foul on the edge of the area, allowing the hosts to increase the pressure.
However, the 2011 and '12 champions could not find a breakthrough, succumbing to their first defeat to Markus Weinzierl's men, much to the disdain of the home faithful, who booed their team off the field.
In contrast, Augsburg are now on a run of three consecutive league victories, defying their pre-season critics to move into the UEFA Champions League spaces ahead of Bayer Leverkusen, who continued their own bid for a top-four finish with a 1-0 win away to relegation-threatened Hertha BSC.
A second-minute penalty from captain Rafael van der Vaart saw the visitors on their way, before second-half strikes from Marcell Jansen and Zoltan Stieber wrapped up the win, which gives Josef Zinnbauer's side a two-point cushion above the relegation zone.
Werder Bremen secured their third straight win with a 2-1 victory at Hoffenheim, while Cologne were held to a 0-0 draw at home to Stuttgart.
