The Bundesliga champion cruised into the DFB Pokal final thanks to goals from Mandzukic, Robben, Shaqiri and Gomez, meaning a historic trophy haul remains a possibility.
Mario Mandzukic, Arjen Robben and Xherdan Shaqiri were also on target for Die Roten, as they disposed of the visitors, who briefly threatened to get back into the contest thanks to a fantastic strike from Diego just before halftime.
With the Bundesliga title secured and a massive Champions League semifinal with Barcelona on the horizon, Bayern remained in the hunt for an historic treble. Despite resting the likes of Franck Ribery, there was no let-up from the Bavarians as they went straight on the offensive, hungry for victory.
With just a handful of minutes on the clock, Die Roten almost opened the scoring. An intelligent pass from Robben opened the right flank for Phillipp Lahm, and the Bayern captain fired low into the box. Bastian Schweinsteiger was on hand to meet the ball, and his first-time effort slipped agonizingly past the near post. It would not be long, however, before the hosts were on target.
Despite matching the champions across the field, Wolfsburg always looked vulnerable when their rivals countered; and it was a swift break that yielded the first goal. Shaqiri held on to the ball just long enough to release Robben on the overlap, and the Dutchman's pass was met by Mandzukic, who smashed into the roof of the net to give his side the perfect start.
With 35 minutes gone, Shaqiri capped another break to play in Robben, and the provider turned scorer as he deftly chipped past Diego Benaglio to double the lead.
Wolfsburg did not despair after falling two behind, and stepped up its efforts to come back into the game. On the stroke of halftime, the visitors got what they were looking for. Taking the ball on the edge of the area, Diego chose to go alone and hit a wonderful strike that gave Neuer no chance, cutting Bayern's advantage and giving Wolfsburg a lifeline for the second 45 minutes.
Buoyed by that strike, Wolfsburg came out after the interval in an aggressive, ebullient mood and looked to level the game. Bayern's attack, however, altered those plans. A short corner from Thomas Muller went to Robben, and the winger reacted well to open up the game for Shaqiri on the edge of the box with a raking pass. The Switzerland international had time to pick his spot, and smashed his effort along the floor to nestle in the corner of the net, adding Bayern's third and putting one foot in the final.
Wolfsburg never stopped trying to get back in the game, but could not find a way to go as time steadily ran out for the visitors. Bayern had few problems in seeing out what remained of the match, as it continued the march onward to a domestic double. Gomez capped a dominant display by netting a simple tap-in at the end and then converting a Schweinsteiger pass shortly afterward to leave the home fans ecstatic as they saluted their heroes in full voice.
Gomez still wasn't done, though, and he sealed his hat trick with another cool finish to complete Wolfsburg's humiliation.
The Bundesliga champions booked their place in the final of the DFB Pokal, where they will face either Stuttgart or Freiburg, who play on Wednesday.