From the first whistle, it did not go according to script for the Los Blancos. The visitors seized the initiative and should have struck early, only for Dayot Upamecano to miscue from point-blank range after meeting Harry Kane's knockdown. That let the hosts settle, and they soon looked dangerous on the break, with superb stopper Manuel Neuer called into action to thwart Kylian Mbappe's effort after a clever through ball from Arda Guler.

Neuer, who produced nine saves on the night, was a wall. The veteran denied Mbappe once again, then produced an outstanding diving save to keep out a fierce Vinicius Junior effort destined for the bottom corner.

Despite those warnings, it was Bayern who found the breakthrough just before the interval. A slick, incisive move sliced through Madrid's defence, and Serge Gnabry's perfectly weighted pass allowed a composed Luis Diaz to fire the ball home

In the second stanza, any hopes of a Madrid response were dented almost immediately. Michael Olise danced past defenders and teed up Kane, who rifled a precise strike beyond Andriy Lunin from the edge of the box. Lunin did well to prevent Olise from adding a third soon after, and Madrid gradually began to gain a foothold.

A defensive error handed them a lifeline when Upamecano's clearance fell straight to Vinicius, but the Brazilian couldn't convert after rounding Neuer, while Mbappe narrowly missed the target with a curling attempt.

Madrid's persistence finally paid off with 15 minutes remaining, as Trent Alexander-Arnold's low delivery finding at the far post, and his effort crossed the line despite Neuer's desperate intervention.

Madrid pressed forward in search of an equaliser but failed to convert as Die Roten earned a famous victory.

Real Madrid head coach Alvaro Arbeloa heaped praise on the brilliant Neuer, who was arguably the difference between the two heavyweights on the night.

"I think he was the MVP, so we had so many chances to score some more goals," said Arbeloa.

We couldn't do it, but we are still alive and we will go there with hope that we can win in Germany. It's not going to be easy. I played there many times and we know the atmosphere in the Allianz is not easy for the opponents. But we are Real Madrid, so we can win anywhere."

Meanwhile, Bayern Munich head coach Vincent Kompany is backing his charges to do the double over Real Madrid.

"The few chances that I feel we should have put to bed, we will be able to score when we go to the Allianz," he said confidently.

"But I see no reason for us not to go into that next game with full belief and an idea to just go and win the game, although we play against a team with incredible talent."

Real Madrid's Toni Kroos undecided on retirement amid great form