Bayern recalled Niklas Sule, Robert Lewandowski, Leroy Sane and Corentin Tolisso from the shock 1-1 draw against Union Berlin last Saturday.
Maximilian Phillip had Wolfsburg off to a flying start inside five minutes after volleying a teasing cross from Mbabu inside the area into the ground and the back of the net.
Bayern were on the receiving end of a flurry of chances thereafter, but Lewandowski in particular was unable to make it count in his side's favour.
The Polish forward finally made his presence felt deep in stoppage time after he popped up unmarked at the far post to turn home Kingsley Coman's curling cross from the left-side.
Bayern turned the game around five minutes in the second half when Lewandowski pounced on a mistimed clearance to race goal-wards for a composed finish.
The Bavarians looked to add to their tally 53 minutes in from a tight angle through Serge Gnabry, but the latter fired wide of the mark.
Hansi Flick turned to the substitutes' bench in the last 20 minutes with Marc Roca introduced for Tolisso and Gnabry making way for Jamal Musiala.
Musiala went close to give his side a third just minutes from appearing off the substitutes' bench, but fired way off target.
Two massive saves from Bayern goalkeeper Manuel Neuer in the last two minutes denied Wout Weghorst from inside the area and Bartosz Bialek from a corner-kick in quick succession.
In the end, the Bundesliga champions ran down the final few seconds to return to winning ways in the league.