The win on Saturday ended a streak of three straight victories for Bayern in this annual match, which pits the winners of the previous season's Bundesliga and German Cup titles.
The duel was electric from the start, more than might be expected in the first days of August, reports Efe news.
Dortmund had more opportunities in an evenly contested first half, with Bayern superstar Robert Lewandowski unable to assert his presence in the centre of the field.
Thomas Muller finally got off a shot for the Bavarian giants in the 19th minute, but it sailed over the crossbar.
Dortmund, meanwhile, tested Bayern goalkeeper Manuel Neuer, who managed to keep the game scoreless with a foot save of a shot by Raphael Guerreiro.
The evenness of the match unraveled as soon as the second half began. Just three minutes had passed when Thiago lost control of the ball and Bayern paid the price. Sancho made a speedy counterattack down the side, booted the ball across to where Alcacer took control straight in front of the net and drilled it in for the score past Neuer, who found it unstoppable, to take a 1-0 lead at the 48th minute.
Bayern tried to battle back, but Marwin Hitz made an outstanding save to deny a shot by Kingsley Coman; Joshua Kimmich then made a strong run but sent his shot off target.
Those missed chances proved costly when Sancho intercepted a pass by Jerome Boateng, raced down the field and beat Neuer with a crossing shot to give Dortmund an insurance goal at 69th minute.
That would be all the scoring Dortmund would need for a 2-0 victory and the club's sixth German Supercup title.
( With inputs from IANS )