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Olise was the provider as Nathaniel Brown marked his competitive Bayern debut with the opening goal, then he added a nonchalant finish of his own just before half-time.

Niko Kovac's Dortmund, which was playing on home soil at Signal Iduna Park, put up more of a fight in the second half and teed up a grandstand finish through Fabio Silva's goal off the bench.

But Dortmund ended the match with 10 men as Bensebaini saw red for his lunge on another Bayern debutant, Ismael Saibari, but it still squandered one huge chance to take it to penalties, via Maximilian Beier.

Amid a low-key start, neither team truly threatened in front of goal until the 28th minute when Vincent Kompany's Bundesliga and DFB-Pokal champion took the lead.

Olise brilliantly took Joshua Kimmich's raking pass down on his chest before slipping the ball into Brown, who finished low past Gregor Kobel.

Kobel kept Dortmund's deficit at one when he sprung to his left to keep out Luis Diaz's drive, and Kovac's side was denied an equaliser by the offside flag when Bensebaini headed home at the other end.

Brown was close to getting his brace for Bayern soon afterwards, but it Olise who got the second goal in first-half stoppage-time, latching on to a loose pass from Jobe Bellingham before weaving his way into the area and finishing with the outside of his left boot.

Having only had one shot in the first half, Dortmund showed more impetus after the break with Konstantinos Karetsas forcing a sharp save from Manuel Neuer, and Silva got it back in the contest with 15 minutes to play, finishing from Daniel Svensson's left-sided centre via a slight deflection.

Dortmund's hopes of a fightback suffered a major blow when Bensebaini received his marching orders, though Beier still should have sent the contest to spot-kicks when he blazed high over Neuer's crossbar from inside the six-yard box in the 93rd minute.