Ji Dong-Won scored in the 45th minute for Augsburg and Sascha Molders made it 2-0 in the 79th minute before Igor de Camargo made things interesting with his goal two minutes into injury time.
Augsburg have lost just one of their last seven matches to improve to 18 points and overtake Hoffenheim, who have just one win in their last 13 matches and remain on 16 points.
There was very little attacking from either team in the opening stages.
Hoffenheim had a chance in the 25th minute as Augsburg keeper Mohamed Amsif's attempted clearance met the head of home striker Eren Derdiyok and just wide of the goal.
The hosts were close in the 38th minute but Daniel Baier's rebound attempt went just wide. And Ja-Cheol Koo's long-range attempt four minutes later was also just barely off target.
Augsburg found the back of the net in the 45th minute as Matthias Ostrzolek's long cross from the left side was volleyed superbly in by Ji at the near left post.
The hosts nearly doubled the lead after 62 minutes but Molders' header off an Andre Hahn cross went just wide.
Koo was close again for Augsburg two minutes later but his looping shot went just over the bar.
Hoffenheim finally had a chance in the 68th minute but Stephan Schrock shot wide left despite having space in the area.
Molders finally doubled Augsburg's lead in the 79th minute with a left-footed snapshot following a through ball by Koo.
Hoffenheim pulled a goal back two minutes into injury time as Joselu found De Camargo, who unleashed a left-footed blast.
But it was too little too late for Hoffenheim.