When the dust kicked up by an utterly scintillating two-legged struggle had settled, Bayern Munich could bathe in the glow of a win for the ages and linger dreamily on the prospect of a semi-final against Paris Saint-Germain.

It is the tie most neutrals wanted but the bar for entertainment has been raised sky high now. Real Madrid should curse themselves, and one of their number in particular, for letting things career out of their control at the death; the sadness for those with no skin in the game came from being deprived an additional half-hour of the near ceaseless thrills both teams were serving up here.

Not that there was anything to scorn about the goals that meant Bayern, behind three times on the night and seemingly heading for extra time, finally shrugged off a flawed but occasionally brilliant Real challenge.

Luis Díaz had been struggling to match his industry with a finish but, given space to have a crack by Jamal Musiala’s whip-smart backheel, took aim from 20 yards. His shot snicked off Éder Militão and ripped into the far corner, Michael Olise then weaving inside and wafting in a sublime clincher just before the close. It was the most fitting way for these 180 minutes to sign off but that did not prevent Real from seething.

The end product of their rage was a red card for Arda Guler, who had been substituted earlier but confronted the referee Slavko Vincic on his way down the tunnel. What a shame that Guler’s night, hitherto notable for two goals that showcased his masterful technique, will now be remembered with an asterisk. It was of a piece with the indiscipline that ultimately cost Real, who had been pushing for a winner in a match that looked impossible to call.

Their anger stemmed from the sending-off of Eduardo Camavinga, who had arrived as a substitute just before the hour, in the 86th minute when the aggregate score was deadlocked. Camavinga had already been booked when, after being penalised for fouling Harry Kane, he carried the ball away in his arms. He dropped it right under Vincic’s nose and, even if it was not the most egregious example of timewasting, his stupidity had forced the official into a decision. Vincic played it by the book with a second yellow card; Real were up against it now and Díaz turned the screw almost immediately.

“It’s unbelievable that you can send off a player for this action in a match like this,” said the Real manager Álvaro Arbeloa. “We feel really upset, really angry, really disappointed. This felt like a defining game in our season.”

It certainly was, which makes Camavinga’s deeply unserious display all the less excusable. Real will end the campaign empty handed but their prospects had looked markedly different when, with only 35 seconds played, Guler levelled a tie that had already delivered richly at the Bernabéu. He was gifted the chance by Manuel Neuer, who had received a backpass from Joshua Kimmich before returning the ball into empty space. Guler meted out instant punishment by finding the vacant goal from 40 yards; Bayern were pegged back but, not for the last time, found a clarity that counted.

“The hardest thing when you concede a goal [at that point] in this kind of game is to press the reset button,” Vincent Kompany said. But they did, receiving assistance of their own when Andriy Lunin failed comically to deal with a Kimmich corner and allowed Aleksandar Pavlovic to nod in from near the line.

Chances came and went regularly, Bayern dictating the tempo and working Lunin harder but frequently dealt warnings by Kylian Mbappé and Vinícius Júnior on the break. It was Guler who struck another blow, bending a hotly disputed free-kick over the wall and seeing an off-key Neuer help his effort in with a glove.

Kane quickly stroked his 12th Champions League goal of the season past Lunin after Dayot Upamecano had been allowed to wander forward and locate him. He has been in a foot race for the golden boot with Mbappé, who made it 15 before the interval when converting exhilaratingly on the run after Vinícius had shuttled down the left. Vinícius had just dipped a shot against the top of the bar; it had been an extraordinary, intensely captivating first half.

Kompany had been booked for protesting about an apparent foul on Josip Stanisic in the buildup to Mbappé’s goal. He will be banned from the touchline for the first leg against PSG and made his dissatisfaction clear afterwards. But it was Real who gradually lost their heads after the interval while the near misses continued to flow, Neuer redeeming himself with a marvellous stop from Mbappé and Olise making Lunin tip over. An irascible Antonio Rüdiger was already treading a fine line before Camavinga crossed it and paid dearly.