The Pole, who found the back of the net threes time against Borussia Dortmund on his last league outing at the Allianz Arena, took just 39 minutes to repeat the feat here.
Serge Gnabry also got on the scoresheet in a rampant first half as Hansi Flick's side brushed off the early loss of Alphonso Davies to a red card to claim a thumping victory.
Davies received his marching orders after VAR intervened to upgrade a yellow for his studs-up challenge on Wataru Endo.
After surviving an early storm, Bayern went ahead through Lewandowski, who claimed second place in the Bundesliga's all-time top scorer charts outright by powering in Gnabry's low cross to bring up his 269th goal in the competition.
A minute later, Lewandowski's powerful header from Muller's right-wing cross had Bayern three ahead with barely a quarter of the game gone.
And the prolific Pole had a hat-trick just before the break, pinching the ball inside the box and arrowing a left-footed finish into the bottom right-hand corner to make it three goals from three shots.
Bayern's number nine should have made it four just past the hour mark but miscued in uncharacteristic fashion after being picked out by Benjamin Pavard's low cross.
But that miss mattered little in the end as the champions saw out their win with little discomfort.
What does it mean? History beckons for Lewandowski
Having already scored more Bundesliga hat-tricks than any other player in history, Lewandowski added a 13th here to extend his lead over Mario Gomez (10) to three.
The Pole is now on 35 league goals for the season and will surely have his sights set on breaking Gerd Muller's record of 40 in a single campaign in the German top-flight in the eight remaining games.
In fact, 'Der Bomber's' outright scoring record of 365 does not look out of reach for a player who is now on 271 and, at the age of 32, still looks to have plenty of years at the top level left in him.
Lewa stars for Bayern
Bayern had been up against it even prior to losing Davies, but the complexion game changed entirely when Lewandowski took his first goal in brilliant fashion.
That the Poland international grabbed his hat-trick from just three shots says everything about his quality in front of goal.
Davies errs again
But for the brilliance of Lewandowski, Davies' rash early challenge could have put his teammates in for a difficult afternoon.
The Canadian had already given the ball away four times in just 12 touches across an uncertain start, and will now miss the crucial showdown with RB Leipzig next time out due to suspension.
Bayern Munich could take a big step toward to retaining the Bundesliga title when they face nearest challengers Leipzig in two weeks. A win would take Flick's men seven points clear with as many games remaining, while defeat would close the gap to just a single point.
As for Stuttgart, they will hope to get their push for European football back on track when they host Werder Bremen.