Robert Lewandowski opened the scoring just after the half-hour mark from the penalty spot to register his seventh league goal of the campaign.
Arjen Robben's shot was then deflected in by Rafinha for a second as Carlo Ancelotti's side raced into a two-goal lead at the break.
Replacing the injured Manuel Neuer, Sven Ulreich then made a mess of Maximilian Arnold's long-range free-kick to give the visitors a lifeline.
An improbable turnaround was completed seven minutes from time when Daniel Didavi headed home, with Mats Hummels missing a last-gasp chance to win it for the hosts.
The home side started in ominous fashion with Arturo Vidal and Jerome Boateng both seeing goal-bound efforts blocked inside the opening few minutes.
Wolfsburg soon found their shape, though, and kept Bayern's formidable attack at bay with surprising ease in the opening half hour.
They even managed to carve out a half-chance of their own, but Arnold was unable to keep his left-footed strike from long distance on target.
The breakthrough came in the 33rd minute – and in fortuitous circumstances – when Lewandowski went to ground easily as he attempted to turn Marcel Tisserand inside the area.
The referee was convinced he had been fouled and the prolific Poland international picked himself up to slot past Koen Casteels from the spot.
There was also a huge slice of luck about Bayern's second, which arrived just before the break.
Robben drove towards the area and the Dutchman's low strike was diverted past a helpless Casteels by the heel of Rafinha.
Early in the second half Robben came close to adding another, but his whipped shot from Franck Ribery's cutback fizzed just over the crossbar.
Wolfsburg pulled a goal back 11 minutes after the interval and it was a moment that Ulreich will want to forget in a hurry.
The 29-year-old inexplicably chose to try to keep out Arnold's free-kick with just one hand, but it offered little resistance as the ball powered past him into the net.
Robben then squandered a golden opportunity to score as he drilled wide with only Casteels to beat.
Ribery blazed over what was practically an open goal with a little over 10 minutes remaining and was made to pay soon after when Didavi met Paul Verhaegh's cross to plant a header in off the post to draw the visitors level.
There was still time for Hummels to head wide from a corner when he really ought to have scored, with Ancelotti's men deflated as the full-time whistle blew immediately after.
Key Opta facts:
- Robert Lewandowski scored his 15th goal against Wolfsburg in 14 games.
- Bayern Munich have scored in each of their last 57 competitive games in the Allianz Arena.
- Arjen Robben scored his 92nd Bundesliga goal (173 games) for Bayern and is now level up with Giovane Elber. No foreign player has scored as many goals for Bayern Munich.
- After more than 13 years Wolfsburg are the first team to claim a point after facing a two-goal half-time-deficit in Munich.