The visitors had the game's first chance in the 15th minute when Ashkan Dejagah volleyed over the crossbar from just eight yards out.
Wolfsburg continued to dominate proceedings at the Gottlieb-Daimler Stadion, but it was Stuttgart who had the ball in the back of the net first.
Maza found the Wolfsburg goal in the 23rd minute but it was ruled out for an infringement.
Vedad Ibisevic came close to scoring for Stuttgart moments later, before Ivica Olic tried to hit back for Wolfsburg.
Bas Dost then thought that he had scored for Felix Magath's side, but his effort was ruled out for a foul he committed in the build-up.
The second half saw both sides go on the attack, and then in the 87th minute Emanuel Pogatetz gave the hosts a great chance to take the lead when he fouled Ibisevic inside the area.
However, Ibisevic's spot kick was saved by Diego Benaglio and minutes later it came back to haunt him.
Dost scored the winner in injury time when he headed home Vieirinha's cross to bag all three points for Wolfsburg.