Pep Guardiola's Bayern also lost their first league game of the season as second-placed Wolfsburg trimmed their lead to eight points.
Bayern leaked as many goals in Wolfsburg as in the entire first half of the season as the home side ruthlessly exploited Bayern's numerous errors.
"We put in a huge performance," beamed Wolfsburg coach Dieter Hecking.
"When you want to beat Bayern, you need a day like that.
"The team did everything we talked about and it went 100 percent according to plan."
Netherlands striker Bas Dost gave the hosts a deserved 2-0 lead at the break as his thunderbolt volley crashed into off the post just before the half-time whistle following an earlier goal.
Belgium international Kevin de Bruyne made sure of the three points with two second half goals while defender Juan Bernat scored Bayern's consolation goal.
"We made a lot of mistakes and let them hit us on the counter-attack," admitted Bayern's stand-in captain Bastian Schweinsteiger with Philipp Lahm injured.
"We lost our shape and we lost too many balls, it wasn't our day.
"We have to analyse the performance and do better."
For the first time in three years, Bayern found themselves 2-0 down at half-time on their way to their heaviest league defeat since losing 5-1 at Wolfsburg in April 2009 -- when Wolves won the Bundesliga title.
"They were better in the key moments. After losing too many balls, we couldn't control Wolfsburg's counter-attacks," admitted Guardiola.
There were emotional scenes before kick-off at the Volkswagen Arena with a minute's applause for Belgium Under-21 international Junior Malanda, who was killed in a car crash earlier this month.
The hosts went ahead on their first venture into the Bayern half.
Daniel Caligiuri's long-range cross from the sidelines was squared by De Bruyne and Dost drove his shot past the diving Manuel Neuer with four minutes on the clock.
Wolfsburg's Maximillion Arnold tried to knock Xabi Alonso off the ball from a free-kick on 43 minutes and both players were booked.
The hosts doubled their lead when Bayern's Robert Lewandowski headed a Wolfsburg free-kick into space. Dost latched onto the loose ball and volleyed home in spectacular fashion from the edge of the area.
Wolves went 3-0 up just after the break when Arnold's pass put De Bruyne in behind the Bayern defence and he rifled his shot home.
Bernat gave Bayern some hope when he stabbed his shot past Wolfsburg goalkeeper Diego Benaglio with 35 minutes left.
The Swiss shot-stopper protected Wolfsburg's lead when he palmed Arjen Robben's shot over the bar with 70 minutes gone as the hosts held on for a deserved victory over Bayern, who are bidding for a third straight league title.
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Wolfsburg made the champions look ordinary. Great work.