It was a game that the hosts deserved to be triumphant in, as they were the better side for large parts of the game.
Finnbogason brought them into the lead before half-time, Stuttgart came closest through Daniel Didavi but the post kept him at bay.
Finnbogason continues scoring form
The opening 10 minutes reflected the general feeling that this would be a tight and tense affair until the teams began to feel more comfortable. Long range shots were exchanged and fired over by both, and it was not until a Daniel Didavi free-kick stung the palms of Marwin Hitz that the fans were reasonably aroused from slumber.
Unfortunately for both sets of supporters, this was as good as it got for the opening half hour of the match. Quality was lacking across the pitch and a lack of scoring opportunities and incisive passing meant that the attackers were becoming increasingly frustrated with a lack of service.
Finally, Ragnar Klavan managed to force a shot on target for the hosts. The Estonian centre-back managed to flick a header goalwards, though Przemyslaw Tyton was able to save. That seemed to be the moment that the game was crying out for, and Markus Weinzierl's side were the team to kick on.
Caiuby was played in down the left by Philipp Max, and the Brazilian whipped in a dangerous ball towards the near post. Georg Niedermeier got their ahead of everyone, only to miscue. Alfred Finnbogason managed to pick up the pieces and scuffed his shot into the far corner, past Tyton. A scrappy finish, but that mattered little to Augsburg.
It could have been two-nil just three minutes later, when Caiuby's crossing caused more problems. He picked out Halil Altintop at the back post, whose volley went narrowly over the bar. Didavi nearly snatched the all-important equaliser in the run-up to half-time; his effort crashed off the post and was cleared before an attacker could react.
Augsburg continue to push forward
Stuttgart needed attacking inspiration and called upon the tricky Alexandru Maxim after the break. However, it was Augsburg who were on the front-foot from the off. Caiuby continued were he left off with a mazy run that ended in a shot being dragged well wide.
The second half was taking up a similar pattern to that of the first, with Stuttgart sitting in their shell and leaving their hosts to retain possession. Given the importance of the game to both, it appeared that only Augsburg were willing to take the risks required to secure the win.
Caiuby brought a superb save from Tyton as the half drew on, with the Polish stopper being relied upon to keep his side in the game. The Brazilian was a menace throughout the game, and he was denied against after Tyton denied Ja-Cheol Koo's initial effort.
Their 'keeper's heroics finally spurred on Stuttgart to come forward and try to gain something from the game. Hitz and Max managed to combine to keep out Timo Werner's header, while Artem Kravets was inches away from connecting with a driven cross. Despite their late efforts, the hosts held on to join their Swabian foes on 33 points. Both are now just two points above the relegation play-off points, although the gap increased to six over Eintracht Frankfurt in 17th.