Mame Diouf put Hannover in front against the run of play before Ragnar Klavan headed in an equaliser.
The Bavarians pushed for the win, which would have seen them move into a Europa League qualification berth, but Hannover held on to end their three-game losing streak and put six points between themselves and the bottom three.
Just two minutes in, Andre Hahn sent Ron-Robert Zieler a warning shot from outside the area, but the German goalkeeper tipped the effort over.
Hahn, who on Friday received his first call-up to the Germany national team, then headed over.
In front of the watching Germany director of sport Hans-Dieter Flick, Hahn led Augsburg's assault on victory.
However, the Bavarians fell behind against the run of play when Diouf received the ball inside the area and, with his back to goal, turned to scramble a weak effort in off the inside of the right-hand post.
Halil Altintop shot into the side-netting after another Hahn effort missed the target, Augsburg not needing long to recover from the shock of falling behind.
They levelled 10 minutes into the second half when Klavan rose to meet Tobias Werner's corner from the right and headed the ball into the far corner of Zieler's goal.
Zieler than took centre stage to ensure Augsburg did not find a winner, denying Werner on the hour mark before plucking cross after cross out of the air to ensure Hannover held on for a point, ending a dismal run of form.