The visitors were inspired by Diego in this surprise result at the Signal Iduna Park which, not only gives them much-needed points but puts a big dent in BVB's title hopes
The German champions took an early lead thanks to a brilliantly executed corner by Marco Reus, which was soon cancelled out by a controversial Diego penalty. Naldo then put the visitors ahead with a stunning volley just before half-time.
Dortmund restored parity in the second half after being awarded a penalty of their own which Jakub Błaszczykowski converted. However, it was again Diego who initiated an attack for the away side, delivering a ball through the middle for Dost, who netted the winner.
Jurgen Klopp's team saw midfielder Mario Gotze making his return to the starting XI, after the youngster had missed the last Champions League group encounter against Manchester City.
On the visitors' side, Brazilian midfielder Josue was given the nod by interim coach Lorenz-Gunther Kostner, while Croatia international Ivica Olic started on the bench.
When the match began, the Bundesliga title holders applied their notoriously ferocious pressing game from the first second, eager to stamp their authority on this encounter.
The approach paid off for the hosts, when Reus delivered a fine corner towards main target man Lewandowski from the left. However, it was the spin of the former Borussia Monchengladbach man's corner which awkwardly saw the ball moving past a stunned Diego Benaglio.
In the 10th minute, BVB followed up with another great chance, when Kuba sent a powerful strike towards the target from about 20 yards out, but the attempt was blocked by Naldo. A follow-up by Lewandowski was then cleared by Simon Kjaer.
Meanwhile, the visitors attempted to press Dortmund into making errors, however, due to the champions' strong midfield, the hosts were able to play their usual passing game, but Wolfsburg's opportunity was just around the corner.
Marcel Schmelzer was adjudged to have handled on the line and was sent off by referee Wolfgang Stark. The decision may have been controversial, but there was nothing contentious about Diego's penalty, who got the visitors back on level terms.
Just five minutes later, Wolfsburg made use of their momentum and turned the match around. It was the Brazilian again who was at the centre of everything good for Kostner's side. He found his team-mate Naldo with an indirect free-kick from the right. The former Werder Bremen man brilliantly volleyed the ball into the box from the edge of the penalty area, securing the 2-1 lead on the stroke of half-time.
The game started slow in the second half, until another penalty was given in the 60th minute. Denmark defender Kjaer pushed Lewandowski over, and Kuba did not hesitate, converting the equaliser.
However, hopes did not last long. In the 73rd minute, it was yet again Diego who drove the away side into taking the lead once more. A run on the counter-attack by the in-form Brazilian ended in an accurate through-ball to Dost, who then slid the ball past Weidenfeller into the right hand corner.
Dortmund are now looking to recover from the loss and prepare for their trip to Hoffenheim on December 16, while Wolfsburg were able to further strengthen their hopes of avoiding relegation.