Augsburg, meanwhile, have won two of their last three matches to move one place ahead of their forthcoming opponents in the table.
Surviving relegation is generally the primary aim for a club of Augsburg's size, and Heiko Herrlich certainly appears to be guiding his side to achieving that comfortably this campaign.
In truth it was a hugely uninspiring game, with Florian Niederlechner unquestionably the brightest player on the pitch. The forward is yet to score in the league yet this season and cruelly - but correctly - had his diving header ruled out for offside in the first half. However, the 30-year-old impressively kept his spirit intact, laying the ball on a plate for Iago, who could not miss from four yards out to seal the victory 13 minutes from time.
Herrlich will have been hugely encouraged by how solid his side were defensively yet again, though, with only five sides having conceded fewer goals in the Bundesliga this season. If Augsburg can find a more creative spark, a top-half finish is certainly not out of the question.
Stuttgart, meanwhile, had a blistering start to the season but have understandably slowed down in recent weeks in their first season back in the Bundesliga, having gained promotion from the second tier last season.
Pellegrino Matarazzo's side struggled to create chances in the 1-0 defeat at home to RB Leipzig on Saturday, with Waldemar Anton's strike their only shot on target across the 90 minutes as Dani Olmo's close-range finish for the visitors ultimately proved the difference between the sides.
There is no shame in failing to score against Leipzig at the moment, though, with Julian Nagelsmann's side keeping a clean sheet in each of their last four games and comfortably conceding the fewest goals in the division.
Augsburg may prove a tough nut to crack, too, but Matarazzo will be imploring his players to take the game to the hosts, especially with Stuttgart boasting a far superior record on their travels this season compared to how they have fared at home so far this season.
Augsburg Bundesliga form: DLDWLW
Augsburg form (all competitions): LDWLLW
Stuttgart Bundesliga form: LWWDLL
Stuttgart form (all competitions): WWDLWL
Jeffrey Gouweleeuw is suspended for one match, meanwhile, after picking up his fifth caution of the season during the win at Koln, with former West Ham United defender Reece Oxford likely to continue in defence.
Tanguy Coulibaly is likely to return to the starting XI having only been used from the substitutes' bench in defeat against Leipzig.
Augsburg possible starting lineup:
Gikiewicz; Gumny, Oxford, Uduokhai; Caligiuri, Strobl, Gruezo, Iago; Richter, Niederlechner, Vargas
Stuttgart possible starting lineup:
Kobel; Stenzel, Anton, Kempf; Wamangituka, Castro, Endo, Mangala, Sosa; Gonzalez, Coulibaly
We say: Augsburg 1-2 Stuttgart
With Stuttgart winning four of their seven matches on the road this season, we can see Matarazzo's side edging a closely fought match on Sunday.
There is no doubt the Bundesliga newboys have greater offensive quality than Augsburg, which could make the difference on the day.