The three points lift the struggling outfit to a place above the relegation zone, ahead of Saturday's visit to Eintracht Frankfurt.
"We were together the entire week and wanted to give something back to the fans for their support," Danso said, as reported by his club's official website.
"We threw everything at it and got a deserved victory as a result.
"Now we need to take this momentum forward with us into the next game."
Danso has so far made six league appearances for Augsburg - all starts - since making his debut last month.
Days after making his senior bow, he was handed a maiden pro deal, which keeps him at the WWK Arena until 2021.
The 18-year-old remains eligible to represent all three countries at senior level, although he currently plays for Austria's under-19 side.