Then, Arturo Vidal was controversially dismissed, and in extra time, an offside Cristiano Ronaldo scored what proved to be the decisive goal of his hat trick in what had been an enthralling match.
Ronaldo scored his hundredth goal in the Champions League and made it a hat-trick by the end of the match which was also his forty first hat-trick for Real.
Poland forward Robert Lewandowski, who missed the first leg with a shoulder problem, had put the Germans ahead on the night from the penalty spot to level the tie on aggregate following Real's 2-1 win in Munich, where Ronaldo had scored twice.
"Controversy? That's football, there in Munich, they were awarded a penalty that wasn't one".
Much like the first leg, Madrid weathered the early storm and had plenty of chances to go in front before half time. But the linesman (on the top of the screen) was well behind the run of play and not even in a position to make the call.
The Portugal captain tapped in the third - for his 100th Champions League goal - after Marcelo's marauding run, with Marco Asensio sealing victory by firing into the bottom corner. Congratulations to the incompetent linesmen.
"The (red) card for Arturo wasn't a card and then the two goals from Cristiano are offside so clearly we are not happy".
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"I think we deserved more", fumed Ancelotti. "Now, Madrid continue and I wish Zizou and his side all the best".
Madrid defeated city rival Atletico Madrid in the final both in 2014 and 2016.
However, a diving header from Ronaldo with 14 minutes left looked to have been enough to send the Spanish side through, only for a freaky own goal from Real captain Sergio Ramos to level things up at 3-3 overall.
Bayern also played the final 30 minutes at the Allianz Arena last week with 10 men after Javi Martinez's dismissal.
Madrid were once again grateful to Ronaldo's killer touch as the four-time World Player of the Year was pivotal in both legs against Bayern. For a game of this magnitude I really don't understand it, a game between two the greatest teams in the Champions League is decided, ultimately, by a group of referees.
Sheer relief greeted the final two Madrid goals as their jubilant players wildly celebrated reaching a record seventh successive semi-final in Europe's premier club competition. You did not need to see a video to see that Vidal got the ball.