The home side had recorded just 14 points all season, winning four games and possessing a -17 goal difference. Meanwhile, their visitors from Bavaria had just seven points more after an uncharacteristically poor start to the season.
Breaking the deadlock
After a somewhat subdued start to the game, it was Augsburg who took the lead on the quarter-hour mark courtesy of a wonderful finish from Ja-Cheol Koo.
The South Korean received a wonderful pass from Caiuby that set him through, but he still had a lot to do as he cut inside and fired past 'keeper Ron-Robert Zieler.
The start was one that the visitors had been craving; a chance to defend a lead, an opportunity that hadn't been so common this season. Meanwhile, the home crowd grew restless, and this seemed to play right into the hands of Markus Wienzierl's side.
In the 29th minute, Alexander Esswein surrendered a big chance to make it 2-0 to FCA as they broke leaving a five-on-two situation. Esswein managed to get a shot away, but Zieler was well positioned to save and thwart the danger.
Hannover threatened most seven minutes before half time when the ball bobbled around inside the box with nobody able to stab the ball home. The home side failed to register a single shot on target in the first half, while the visitors had just one.
After a couple of early bookings and a scrappy start to the second half, it was Augsburg who began probing once again. Attempts from Leroy Sane and Ji failed to really trouble the goal.
On the hour mark Augsburg had a chance to double their lead as Esswein crossed onto the head of Ji, but it was sent over the bar in what was a piece of respite for a struggling Hannover side.
Tobias Werner was introduced by Wienzierl with 20 minutes left on the clock, and in the 77th minute he had a chance to kill the game, though Zieler saved again to keep the deficit at one.
Hannover thought they had a late equaliser when Hugo Almeida bundled home, though he was correctly adjudged to be in an offside position.
Koo struck an 84th minute effort goalwards, but it just drifted wide ensuring the last few minutes would be nervy.
There was to be late drama as Hannover got a 93rd minute corner, which was swung in by Hiroshi Kiyotaki, and Alexander Milosevic met it with his head, yet Marwin Hitz somehow kept it out.
The game ended at 0-1, and a vital three points for Augsburg propelled them to 13th with 24 points, just three points behind Hamburger SV in the spot above. It also leaves them four points from 16th and that all important relegation play-off spot.
The worries continue for Hannover, who missed a chance to close the four point gap on 17th place Hoffenheim. Instead, they remain rooted to the bottom.