Second-placed Leverkusen came to Munich's Allianz Arena looking for their first win at Bayern since 1989 and to close the five-point gap behind league leaders Borussia Dortmund, who face Freiburg later on Sunday.
But Bayern bounced back from last Sunday's sacking of coach Louis van Gaal to floor their guests and end Leverkusen's five-game winning streak.
An own goal by Leverkusen captain Simon Rolfes, Gomez's treble and a fine individual goal from France's Franck Ribery did the damage for Bayern.
Germany star Bastian Schweinsteiger and goal-scorer Ribery both brushed off pre-match injuries to play their part in the rout and hand caretaker coach Andries Jonker his first win in charge.
"We took our chances in a ruthless fashion and, certainly in the first half, we played with a high level of aggression," said Jonker.
"The boys had clearly understood the message and they did what had to be done."
Ironically, Levrkusen coach Jupp Heynckes will take charge at Bayern next season and he was given a front-row seat as his team were dismantled.
The guests fell behind after only seven minutes when a corner from Schweinsteiger deflected off Rolfes' face and into his own net.
Chile midfielder Arturo Vidal then gave away possession in his own area and Bayern's Thomas Mueller reacted fastest to square the ball to Gomez, who fired home on 28 minutes.
The Germany star needed only 18 more minutes to complete his hat-trick, which leaves him as the Bundesliga's top scorer with 22 league goals this season and 33 in all competitions.
He wrapped up his hat-trick on the stroke of half-time to leave Leverkusen 4-0 down and shell-shocked at the break.
The guests pulled one back through Swiss striker Eren Derdiyok with an hour gone, but Ribery, who was superb throughout, fired home on 75 minutes to complete the rout.
With four games left, Bayern are now up to third -- on course for a Champions League place next season -- and just six points behind Leverkusen.
"Every single one of the 11 players played their role," said captain Philipp Lahm.
"It was important that Hanover drew, Leverkusen are still too far ahead for us to claim second, but we need to concentrate and make sure we stay in third."
On Saturday, Champions League semi-finalists Schalke 04 came from behind to rescue a 1-1 draw at Werder Bremen to leave both sides in mid-table.
A late equaliser by VfL Wolfsburg secured a 2-2 draw at home to St Pauli to give the 2009 Bundesliga champions a fighting chance of escaping the relegation zone. Wolves are four points from safety with four games left.
Hanover 96 are fourth in the league after they were held to a goalless draw by Hamburg.
Stuttgart pulled away from the relegation zone with a 3-1 win at Cologne to put four points between themselves and the bottom three.
Hoffenheim moved up to ninth as Brazilian teenager Roberto Firmino scored his first goal for the club with a 78th-minute strike after being set up by ex-Liverpool forward Ryan Babel to earn a 1-0 win over Eintracht Frankfurt.
On Friday, Mainz's Germany striker Andre Schuerrle scored a late goal to give his side a 1-0 win over 10-man Borussia Moenchengladbach and keep his team fifth and on course for a place in Europe.
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