The 2011 and 2012 Bundesliga champions looked devoid of ideas throughout and continually lacked a final pass in front of a sold-out 80,000 home crowd and were easily outmuscled by European hopefuls Augsburg with Raul Bobadilla netting the 50th minute??winner.
Surprise packages Augsburg, who moved up to fourth, had Christoph Janker sent off midway through the second half, but were able to shut out Dortmund with relative ease over the closing half hour.
Dortmund, who take on Juventus in the Champions League round of 16 this month, are bottom on 16 points after their 11th league loss this season.
Hamburg eased their relegation fears after they beat Paderborn 3-0, ending their league goal drought after 398 minutes.
Rafael van der Vaart converted a penalty after Hamburg were awarded the fastest Bundesliga spot-kick this season just eight seconds into the game.
Goals from Marcell Jansen and Zoltan Schieber made sure of the three points and lifted Hamburg to 13th.
Bayer Leverkusen edged past Hertha Berlin 1-0 to move into fifth, a point behind Augsburg, while Werder Bremen won 2-1 at Hoffenheim and Cologne played out a goalless draw with Stuttgart.