England's captain hit the target yet again after going on as a second-half substitute on Sunday, and Bayern could easily have scored more against the overwhelmed Stuttgart defence as they moved an unassailable 15 points clear of second-placed Borussia Dortmund with four rounds of the German league remaining.
It was Bayern's record-extending 35th German championship, including the first for the club in 1932. Every other title came after the Bundesliga's formation in 1963.
Stuttgart's Chris Fuhrich had looked to spoil the script for Vincent Kompany's team with the opener in the 21st minute, but Bayern's Raphael Guerreiro, Nicolas Jackson and Alphonso Davies replied by scoring in a six-minute spell in the first half.
Kane's 52nd minute goal – his 51st of the season across all competitions for Bayern – then stretched the team's Bundesliga record for goals in a season to 109.
The previous record, set by Bayern's 1971-72 team featuring Franz Beckenbauer and Gerd Muller, was 101 goals.
Kane has had his sights on breaking Robert Lewandowski's season record of 41 Bundesliga goals but Kompany decided to manage his star forward's playing time to rest him for key games coming up.
Bayern's players lined up in front of the fans to mark the triumph, but there were none of the traditional beer showers that usually accompany league wins.
For the Bundesliga is just the first in a potential treble of trophies for Bayern this season.
The Bavarian powerhouse face Bayer Leverkusen away for their German Cup semi-final on Wednesday, and then they have a two-legged Champions League semi-final tie against defending champions Paris Saint-Germain.
"It is wonderful. These moments follow a lot of work. We have to enjoy it," Kompany said after sealing his second German title in his two years in charge.
"Tomorrow it starts again, just like every day. I want to enjoy even more, there is always more. We can still win things."
Matching Bayern's six titles out of six in the 2019-20 season is now a clear goal.
"It is April 19 and we are in every competition. We have had lots of success with every player in the squad. We go to Leverkusen knowing anything can happen, but with real belief."
The atmosphere was muted at the start of the game. There was a clash between Bayern and Stuttgart fans before the match, causing some fans to miss it altogether.
