Bayern Munich laid down a marker for the new season as they beat Klassiker rivals Borussia Dortmund 2-1 to win the German Supercup at Signal Iduna Park.

Nathaniel Brown, who made a big-money summer move from Eintracht Frankfurt, broke the deadlock in the 28th minute when he swept in a cross from Michael Olise.

France forward Olise clipped home a second in first-half stoppage time to put the Bundesliga champions in control.

Fábio Silva pulled a goal back for Dortmund with 15 minutes left before Ramy Bensebaini was shown a late red card for a rash tackle.

Bayern came through a spell of pressure from the home side, with Maximilian Beier firing over, to pick up what they hope will be the first trophy of another successful campaign.

Germany winger Jamal Musiala missed the match as he continued his recovery after a change in his medication for a neurological condition saw him twice collapse during Bayern's preseason friendlies.

The Bundesliga champions made a positive start looking to dampen the partisan home support as Aleksandar Pavlovic's first-time shot was straight at Dortmund keeper Gregor Kobel, who then recovered to gather a long-range lob from England captain Harry Kane.

Bayern went ahead in the 28th minute. A pass down the middle found Olise in the Dortmund box and he laid the ball back for Brown to slot in his first competitive goal for Bayern.

Luis Díaz then cut inside from the left and his low, curling effort was palmed away by Kobel before Brown dragged a shot across the face of goal.

Bayern did double their lead in stoppage time at the end of the first half when Olise got into the right of the penalty area and looked to have lost control of the ball only to slot it into the far corner.

Dortmund improved in the second half as substitute Giannis Konstantelias, the Greek winger signed in the summer from PAOK, saw his volley deflected behind.

Bayern then failed to deal with a corner and Konstantinos Karetsas' left-footed snapshot was saved down low by Manuel Neuer.

Dortmund pulled a goal back with 15 minutes left when Silva swept home a cross from Daniel Svensson following a break by Konstantelias down the left.

Kane then curled a 20-yard effort just wide before the home side went close again when Silva planted his header straight at Neuer.

Bensebaini -- who had been struggling with injury, but Dortmund had no substitutes left -- was shown a straight red card for a late challenge on Ismael Saibari.

Olise was sent racing clear in stoppage time but could not find a finish to beat Kobel, before Dortmund almost snatched a dramatic late equaliser when Waldemar Anton's lofted pass found Beier in the six-yard box and he fired the ball over.