The hosts, meanwhile, enter the match six points ahead of Arminia in the table, so will be looking to win to end any lingering relegation fears.
Heiko Herrlich would have been desperately disappointed to have become only the second side to be beaten by Schalke 04 in the Bundesliga this season after falling to a 1-0 defeat to the rock-bottom outfit last Sunday.
Generally, Augsburg prefer to hold onto a lead rather than chase one, but their performance actually merited at least an equaliser against the division's most accommodating defence.
Richter was guilty of a far worse miss after the half-time interval, somehow blazing over from close range after Raphael Framberger had brilliantly bustled down the right flank before accurately crossing the ball into the path of the 23-year-old.
Clearly desperate to score, Richter was unfortunate to see his acrobatic overhead kick saved by Fahrmann late on, with Augsburg falling to a damaging defeat.
Herrlich will be demanding more ruthlessness in front of goal against an Arminia side who have not been conceding many chances of late and will be scrapping for their lives, particularly as another defeat could drag Augsburg right into the relegation mix.
Die Arminen may not be as pleasing on the eye as they were at times under their predecessor, but there can be no denying that they now appear to be a more likely prospect to survive relegation in their first season back in the Bundesliga.
While there was an element of fortune regarding the way their 1-0 win at home against Freiburg last time out came about, with Masaya Okugawa's effort deflecting off Baptiste Santamaria and beyond a helpless Florian Muller in goal, they were deserved winners on the day after a spirited performance.
Kramer will be hoping for a similar performance against Augsburg on Saturday, with the first goal likely to prove crucial between two low-scoring sides.
Herrlich could look to shake things up in attack after a misfiring display in the defeat at Schalke, with Florian Niederlechner offering a potentially more clinical alternative to Richter.
Arminia, meanwhile, will travel without Sergio Cordova, who is on loan from Augsburg, after the striker tested positive for COVID-19 prior to the win against Freiburg.
Reinhold Yabo, who is a close contact for Cordova, has also entered self-quarantine as a precautionary measure, so will not be available either.
Kramer is unlikely to make any changes to the XI which performed so well during last weekend's victory.
Augsburg possible starting lineup:
Gikiewicz; Framberger, Gouweleeuw, Uduokhai, Gumny; Khedira, Gruezo; Caligiuri, Vargas; Niederlechner, Hahn
Arminia Bielefeld possible starting lineup:
Ortega; Brunner, Pieper, Nilsson, Lucoqui; Prietl, Maier; Doan, Okugawa, Voglsammer; Klos
We say: Augsburg 1-1 Arminia Bielefeld
Recent form suggests Augsburg will win this match given that they are currently on a streak of win, loss, win, loss, win, loss, but we can envisage that ending with a low-scoring draw between two evenly-matched sides.
Arminia look a much more solid proposition under Kramer, with a point potentially taking them out of the bottom three, depending on how Hertha Berlin fare against Mainz 05 in the weekend's big relegation clash.