Bas Dost scored twice in the first half and Kevin de Bruyne added two more goals after the break as Bayern, who had conceded only four times in the first half of the season, saw their goals against tally double in a single game.
Juan Bernat replied for the Bavarians 10 minutes into the second half.
Wolfsburg, with 37 points from 18 games, have cut Bayern's lead to eight points, although it would still take a dramatic turnaround for the title holders to be caught.
It was an emotionally charged evening as both teams paid tribute to Junior Malanda, the Wolfsburg player killed in a car crash earlier this month, in a ceremony before kickoff.
The Belgium youth international died when the car he was a passenger in went off the motorway and flipped over several times on Jan. 10.
CAUGHT COLD
Bayern, who won the same fixture 6-1 last season, were caught cold in the fourth minute after an attack broke down.
Wolfsburg switched the ball to Daniel Caligiuri and he threaded a delightful ball to de Bruyne who passed it on for the unmarked Dost to open the scoring after four minutes.
Wolfsburg struck again on the stroke of halftime when a Ricardo Rodriguez free kick was poorly cleared by Robert Lewandowski and Dost's volley spun away from Bayern goalkeeper Manuel Neuer and in off the post.
The visitors were caught on the break eight minutes after the restart when Maximilian Arnold sent de Bruyne steaming clear and he fired a low shot emphatically past Neuer.
Juan Bernat pulled a goal back two minutes later and Arjen Robben nearly reduced the arrears further when a screeching effort was turned away by Diego Benaglio.
Instead, Wolfsburg countered again and de Bruyne turned Dante one way then the other before blasting the ball into the roof of the net.
"We played a great game. To beat Bayern you need a day like this. Everything we had planned worked out," Wolfsburg coach Dieter Hecking told ARD television.
His opposite number Pep Guardiola added: "They were the better team and they scored at the crucial moments, at the start and end of the first half."
(Writing by Brian Homewood; Editing by Ken Ferris)
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