Eric Maxim Choupo-Moting should have completed the comeback for Bayern Munich in the 48th minute. But he failed to find the target after being played through on goal by Kane.
And the miss proved to be very costly for Bayern, as Jeong Woo-yeong restored Stuttgart's lead in the 84th minute with a fine header from the back post after getting on the end of Silas' cross.
Silas then turned from provider to goalscorer as he made sure of the three points for Stuttgart with an excellent first-time finish in the 93rd minute. To make matters worse for Bayern, Raphael Guerreiro picked up an ankle injury in the first-half and left the stadium on crutches.
Bayern Munich would have hoped to wrap up second place in the Bundesliga standings with a win over Stuttgart, but now find themselves with some work to do in the final two games of the season.
More importantly, the defeat to Stuttgart will serve as a huge blow to Bayern Munich's momentum ahead of the all-important second leg of their Champions League semifinal against Real Madrid on Wednesday.