The hosts started on the front foot but failed to create anything of note until the 17th minute when Mario Mandzukic gave them the lead.
Arjen Robben raced clear of the Wolfsburg defence and crossed low for the Croatian to fire past his former club.
The away side almost hit back five minutes later when Manuel Neuer could only punch a clearance as far as Makoto Hasebe, but the Bayern keeper scrambled to his feet in time to stop the Japanese international's effort.
However, Diego gave them a lifeline right on the stroke of half time, finding the top corner with a superb strike from the edge of the box that left Neuer stranded.
Wolfsburg's hopes of staging a fightback were dashed early in the second period when Shaqiri got the goal he deserved, lashing a low strike into the bottom corner after being picked out by Robben.
It was easy street for Bayern after their third goal went in, and they extended their lead even further with 10 minutes left on the clock, Gomez turning in Shaqiri's pass from close range to make it 4-1.
Gomez netted his second of the evening two minutes later before completing an astonishing six-minute hat-track moments after that for a final score of 6-1.