Brazilian midfielder struck a winner at the death to earn a valuable victory for the visitors
The hosts started off in bullish form, and their intensity caused no shortage of trouble for Bayern, who lacked a cutting edge in the absence of injured star Arjen Robben.
Patrick Helmes appeared to put Wolfsburg ahead in the 40th minute as he nodded home from close range, and although replays would show that there were two Bayern players between the forward and goal, his strike was nonetheless called back for offside.
To go into half-time behind might have been a bit harsh on Bayern, who did have a couple chances. Most notably, Franck Ribery sent a cross towards Mario Gomez, but Diego Benaglio bravely intervened to grab the ball off the striker's boot. The in-form Ribery also had a penalty claim denied earlier in the half.
Moments after the break, Bastian Schweinsteiger had a chance to put the visitors ahead, but on his unfavoured left foot and with a tight angle from which to shoot, he fired over the crossbar. Toni Kroos found himself with room to shoot in the 57th minute, but struck well wide from inside the area.
In the final quarter hour, the game increased in intensity as both sides sought a winner. Christian Trasch game close for the hosts, who were also denied a penalty claim. In the end, however, it was Luiz Gustavo who made the difference, as he fired a thunderous shot off Benaglio's hands and into the net.
The result sees Bayern win in a less than convincing manner, moving to 11th in the standings. Wolfsburg are still ahead of the Bavarians, and sit fifth in the standings due to superior goal difference.