Martin Harnik gave Stuttgart the lead, but Bayern replied with three goals in a 12-minute spell before half-time, and added three more in six minutes after the break, as the visiting defence did little more than stand and watch.
Thomas Muller scored twice with Toni Kroos, Luiz Gustavo, Mario Mandzukic and Bastian Schweinsteiger sharing the others for the Bavarians, who finished as runners-up in the Champions League, Bundesliga and German Cup last season.
Vedad Ibisevic completed Stuttgart's miserable day when he was sent off for head-butting Jerome Boateng in an ugly incident.
Bayern, also without prolific scorer Mario Gomez and winger Arjen Robben, have hit nine goals in winning their opening two games and, alongside promoted Eintracht Frankfurt, are the only side with maximum points.
Martinez, signed for a reported €40m from Athletic Bilbao on Thursday, and Swiss winger Xherdan Shaqiri, a €12.5m signing from FC Basel, both began on the bench.
Stuttgart, who have lost their first two games, began brightly as Harnik struck the underside of the bar in the fourth minute.
The Austrian striker then put Stuttgart ahead in the 25th minute when Arthur Boka's free-kick found him at the far post and he volleyed the ball over a shocked Manuel Neuer.
It was all downhill from there and Bayern were ahead within eight minutes.
Muller equaliser in the 32nd minute, scoring from the rebound after Sven Ulreich failed to hold his initial shot.
From the restart, Stuttgart lost possession outside their own area and Gustavo laid the ball off to Kroos, who scored with a rising shot from 25 metres.
Gustavo then added the third two minutes before the break when he was given too much space and rifled a dipping 30-metre shot into the bottom left-hand corner.
It got worse after the break. A minute into the second half, Gotoku Sakai lost the ball to Franck Ribery, who found Muller. The midfielder's shot was partially stopped by Ulreich, landing perfectly for Mandzukic, who hit home into an empty goal.
Two minutes later, Stuttgart were caught on the break and Muller walked the ball in after Ulreich could only deflect Mandzukic's attempted chip into his path.
Another two minutes after that, Muller chipped in a cross from the right and Schweinsteiger, completed unmarked, headed in at the near post.
Spain midfielder Martinez came on for his debut in the 77th minute, but Bayern had eased off by then.
In another lop-sided contest, Hannover inflicted a 4-0 home defeat on hapless VfL Wolfsburg with new signing Szabolcs Huszti having a hand in all four goals.
"From the moment they scored we played an outstanding game," said Bayern coach Jupp Heynckes.
"You can see that the players have fun playing football. But above all, this team is in harmony with itself. I am pleased with the 6-1 win, but more how the team performs in their day-to-day work."
Stuttgart coach Bruno Labbadia said his side paid the price for making too many
