Schlotterbeck headed Dortmund ahead in the 26th minute when he rose highest in a crowded penalty area to connect with Svensson’s free-kick from the left.
Dortmund had the chance to double their lead later in the half when Fabio Silva squared the ball to Maximilian Beier, who was denied by the onrushing Jonas Urbig.
Despite dominating possession in the first half, Bayern – playing with a front three of Kane, Michael Olise and Luis Diaz – were unable to test Dortmund goalkeeper Gregor Kobel.
But Kane equalised early in the second period with a poacher’s effort from inside the area at the end of a slick move involving Kimmich and Serge Gnabry.
Both teams missed chances before Kane scored a penalty – a record 10th in a Bundesliga season – after Josip Stanisic was floored by Schlotterbeck.
Dortmund levelled when Svensson volleyed past Urbig, but Kimmich all but ended their hopes of winning a first title since 2012.
