Stuttgart have been relegated from the Bundesliga following their 3-1 defeat at Wolfsburg on Saturday.
The 2007 Bundesliga champions needed a win at the Volkswagen Arena to have any hope of survival after taking just one point from their previous seven games.
Maximilian Arnold and Andre Schurrle, however, scored in the opening half-hour for the hosts to leave Jurgen Kramny's men with a mountain to climb in the second half.
Daniel Didavi fired in a free kick for Stuttgart in the 77th minute, but Schurrle added his second of the game late on to condemn the visitors to the second tier for the first time in 39 years.
Stuttgart's loss was Werden Bremen's gain as the 2004 Bundesliga winners, who would have been relegated had Die Schwaben won, scored a late winner to beat Eintracht Frankfurt 1-0 and secure safety.
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