The rampant Bavarians handsomely avenged their shock 1-0 first-leg last 16 defeat against the Swiss champions to go through 7-1 on aggregate and keep alive their dream of playing the final in their own Allianz Arena stadium.
It was the biggest winning margin in a Champions League knockout round match, Bayern's biggest win in the competition and Basel's heaviest European defeat.
Basel had qualified for this stage at the expense of Manchester United but some dreadful defending meant their hopes of becoming the first Swiss team to reach the last eight for 33 years were in tatters by half-time.
Arjen Robben, Thomas Muller and Gomez put Bayern 3-0 ahead by the break before Gomez added three more in 18 second-half minutes, all provided by Franck Ribery.
That left the striker one goal short of Lionel Messi's record Champions League haul of five in Barcelona's match against Bayer Leverkusen last week.
It was Gomez's second hat-trick in successive games, after his three goals in the 7-1 win over Hoffenheim in the Bundesliga on Saturday, and took his Champions League tally to 10 goals.
Robben completed the scoring with nine minutes left by which time, astonishingly, the sizeable Basel contingent in the crowd were still singing and waving flags.
VERY CLEVER
"We were aggressive, strong and very clever against a team who can play much better than they did today," said Bayern coach Jupp Heynckes, whose side could still win a treble this season.
Basel's clearly shell-shocked coach Heiko Vogel, who suffered only his second defeat since taking over in November, added: "I'm not disappointed that we lost, but I'm enormously disappointed at the way we lost.
"We have achieved a lot, the team has achieved lot and we shouldn't forget this, I don't want our campaign to be reduced to this result."
Basel were unbeaten in their previous 17 matches but playing at a packed Allianz Arena was a far cry from games such as Saturday's Swiss League win over Grasshoppers in front of 7,000 people.
Before the game, Basel had talked of a new self-belief previously lacking in Swiss teams but they disintegrated as soon as they first goal went in.
Bayern, starting without Bastian Schweinsteiger who has only just recovered from an ankle injury, were in a different class.
The German side, clearly stung by their first-leg defeat, Bayern went straight for the jugular and needed only 11 minutes to wipe out the deficit.
Muller's pass was defelcted through the Basel rearguard, leaving Robben with only goalkeeper Yann Sommer to beat which he did emphatically.
REFLEX SAVE
With Robben and Ribery allowed far too much space down the flanks, Sommer kept Basel alive as he twice denied Gomez, followed by a stunning reflex save to turn away Muller's header at point-blank range.
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