André Schürrle scored twice and Maximilian Arnold also got on the scoresheet, with Daniel Didavi issuing a reply for the Swabians.
An historic day in the top tier of German football, as one of the founding members slipped down a division.
Schürrle and Arnold put Wolfsburg in a comfortable position
In what was a fairly even opening in Lower Saxony, both teams were threatening from wide areas. A battle was emerging in midfield but Wolfsburg would find an early way through the Stuttgart back-line. Marcel Schäfer managed to wriggle round Matthias Zimmermann before whipping a devilish ball into the six-yard box. Maximilian Arnold stole a march on his marker and made the Swabians pay, thundering home from close range to leave them with a mountain to climb.
It could have been even worse for the visitors had Mitchell Langerak not came to their rescue, denying Schäfer with his shoulder after the defender had ran through on goal. Stuttgart's only chance after the opening 25 minutes had fallen from a corner and to Daniel Schwaab, though he couldn't find the target.
Even though the game was lacking clear-cut openings, any of which were falling for the Wolves - unfortunately for Stuttgart, they were in clinical finishing form. A breakaway from inside their own area saw Daniel Caligiuri bring the ball away and feed André Schürrle. Their star signing got a kind deflection off Timo Baumgartl, with the ball flying over the helpless Langerak and into the net; relegation was staring the visitors in the face.
It looked like the Swabians would head into the break without any hope whatsoever but they did manage to test Koen Casteels late on. Daniel Didavi brought a sprawling stop from the Belgian goalkeeper, but the best chance fell for Martin Harnik. The Austrian was played in by Artem Kravets and, somehow, managed to rattle over the bar from close range. Signs, at least, that they could come forward in the second half.
Didavi's goal all in vain
The beginning of the second half saw Stuttgart unfurl their 'Keine Ahnung, keine Planung, keine Konzept - VORSTAND RAUS!' banner, but whatever was said at half time seemed to be having a positive effect. The visitors came out firing, but more wasteful finishing and a lack of cutting edge meant they couldn't take advantage of a slow Wolfsburg start.
The hosts had almost given up, in terms of attacking, which left the emphasis on Jürgen Kramny's side to try and force a way through. Try as they might, however, there was nothing but growing anger from the travelling support was becoming more and more audible. That finally seemed to have an effect on the players, and Stuttgart grabbed a goal back.
Didavi took aim from a 20-yard free-kick and curled the ball up and over the wall, leaving Casteels with no chance as the ball nestled in the bottom corner. However, they soon had Langerak to thank for a superb recovery that hooked the ball off the line. Alexandru Maxim's late free-kick looked to have levelled the scores until Casteels managed to tip it over the bar, and Wolfsburg heaped further misery on as Schürrle finished off another breakaway with a chipped finish.
Stuttgart will now spend next season in the second tier, while Wolfsburg finished off the year in ninth.