Conor Hourihane netted two free kicks either side of a Yussuf Poulsen equaliser, whilst John McGinn ensured Villa left Germany with a victory.
There were impressive displays across the pitch for Dean Smith's side, with new signing Tom Heaton standing out in particular with a number of fine saves following his move to B6 this week.
Villa's opener came courtesy of Hourihane, striking with a trademark free-kick from 20 yards out following a foul on Jack Grealish.
The hosts did level in fortuitous fashion after Poulsen pounced, but Villa saw out proceedings with another Hourihane set-piece strike before McGinn finished things off late on with a tidy finish off the post.
Villa will now prepare for their Premier League opener on Saturday - where they travel to Spurs in the evening kick-off.