As a result of the point, Augsburg improved to four points, while Hannover moved to 12 points in the upper third of the table.
Hannover did rattle the frame of the goal twice, but that was as good as it got.
Neither side created much going forwards in the first half, with the only chance coming in the 17th minute when Augsburg's Gibril Sankoh cleared Lars Stindl's shot at the line.
Hannover had the next chance 11 minutes after the half-time break, but Augsburg keeper Simon Jentzsch did a fine job corralling Jan Schlaudraff's long distance blast.
The run of play continued towards the Augsburg goal but Didier Ya Konan's shot went off the post in the 62nd minute.
Hannover were stopped by the woodwork agains four minutes later with Ya Konan hitting the left upright, with Stindl's rebound attempt flashing wide right.
Augsburg finally made some noise in attack after 69 minutes but Akaki Gogia's long-range blast went just wide.
Hannover keeper Ron-Robert Zieler needed a great save to keep his sheet clean two minutes later, stopping Sascha Molders' shot from Marcel de Jong's cross from the left side.
And Hannover failed to grab the victory despite a final chance with four minutes left as Stindl was stopped by Jentzsch.