Maybe because the pressure from Stuttgart supporters who filled the stands at the Mercedes-Benz Arena stadium made the Dortmund players mentally depressed and they could not do much with such a situation, indeed if you think logically this match does not make sense, because previously Stuttgart was also held to a draw by Mainz05 and defeated by Freiburg, which is basically far away from Dortmund's level, but unfortunately Dortmund was even humiliated.
I agree totally with you, even we're were at the academy, our coach back then makes it clear tho it's that a match can be win with an effective supporters club. He stimulates the supporters with such understanding that their support is very instrumental to our winning. Their constant supports goes a long way to demoralize even the stronger team and give us a win. It surely works like magic.
They try their best to distract the opponents with their shouts and songs of support to their choice team, goes wild when the team records a success and don't resist boing the opponents at any slight error. That way, the opponents are demoralized and underperform even without knowing
I think Dortmund supporters should do the same when Stuttgart will visit their home, I see how Dortmund maniacs are also many and they must reply with the same thing to the Stuttgart team later.
And indeed supporters are very important in the match, I myself feel it when I play futsal ball and against a team that brings a lot of supporters, making my mentality often depressed and feeling uncomfortable, and yes it is quite effective in disturbing the players to focus on the game, have you ever felt the same way in a match whose opponent brings many supporters?