Vincent Kompany saw this as an opportunity to rest some of his senior players, with captain Manuel Neuer and talisman Kane left on the bench here.
That approach didn’t appear to hinder them as the Bundesliga leaders snapped a run of conceding first in three successive league matches, breaking the deadlock on 11 minutes in some style.
Stand-in goalkeeper Jonas Urbig started the move with a long ball that was brilliantly controlled by Konrad Laimer, who duly fed Michael Olise before receiving the ball back from the Frenchman and finishing with a gorgeous backheel for his first-ever goal against Stuttgart.
As Stuttgart were one of just three teams to start the round having scored in every game, Bayern’s position was far from safe.
The visitors, therefore, set about doubling their lead, and nearly did so when a curling effort from Olise burst through Alexander Nubel only to trickle wide of the far post. Sebastian Hoeness’ men looked to have levelled proceedings just five minutes before the break, but Nikolas Nartey’s header was chalked off for offside before Chema Andrés fired wide from the edge of the box to ensure Bayern led at half-time for a league-high ninth time this season.
Clear-cut chances came at a premium after the restart, with Olise flashing just over for Bayern before Deniz Undav’s strike at the other end was brilliantly tipped over the bar by Urbig after taking a wicked deflection.
Kompany’s side continued to look the more dangerous, and after Luis Diaz contrived to fire wide when unmarked from close range, substitute Kane needed just five minutes after coming off the bench to double their lead.
Aleksandar Pavlovic won the ball brilliantly in the Bayern half, starting an attack that saw Kane pick the ball up on halfway before sauntering forwards and rifling a brilliant low drive into the bottom corner from 25 yards, netting his eighth goal in six games against Stuttgart.
Only a fabulous save from Nubel denied Kane a ninth H2H strike on 75’, but the goalkeeper was at fault for Bayern adding their third moments later as he let Josip Stanisic’s powerful strike burst through his grasp and in at the near post.
A miserable first scoring blank of the Bundesliga season for Stuttgart got even worse late on when Lorenz Assignon blocked Olise’s goalbound strike with his hand, receiving a red card and conceding a penalty which Kane coolly converted.
The England captain completed his treble by tapping in from Olise’s cross to make it 5-0 as Bayern set a new Bundesliga record, having scored multiple goals in 21 successive matches, with this a 16th victory from their last 17 trips to Stuttgart.
Flashscore Man of the Match: Michael Olise (Bayern Munich)