The Portuguese superstar landed his first leg goal scoring form in the second by scoring a memorable hattrick to cement his name in the all time Champions league greats after becoming the first player to score 100 Champions League goals.
Six minutes after, Madrid got their own gift from Bayern, when striker Arturo Vidal bagged a second yellow card and was sent out of the field.
Madrid is trying to become the first team to defend the title since the competition's new format was created in 1992-93.
Earlier, Leicester City's fairytale Champions League journey came to an end at the King Power Stadium when the English champions were held to a 1-1 draw by Atletico Madrid, who reached the semi-finals for the third time in four seasons with a 2-1 aggregate win.
Ronaldo scored a hat-trick to send Real Madrid through to the Champions League semi-finals.
Nothing separated the two teams over 180 engaging minutes in Munich and Madrid, only for the German champions to finally run out of steam as they battled a numerical disadvantage.
North Korea shows off intercontinental ballistic missiles in parade
It also makes the missiles harder to detect after they're fired, Kim said. "It wasn't a matter of if, it was a matter of when". The timing of the test, coinciding with Pence's trip and a day after the military parade, would suggest deliberate defiance.
Bayern's Arturo Vidal put the hosts ahead in the first half and ballooned a spot kick over the bar, before two Cristiano Ronaldo goals swung momentum in Real's favour.
City took the game to Atletico after the break and gave themselves hope via Jamie Vardy's close-range finish which drew the tie 1-1 on the night but 1-2 aggregate.
They turned up at the Bernabéu having lost 1-2 in the first leg and still managed to force extra-time. Arjen Robben lashed the rebound into the side-netting.
Bayern pushed hard for a second goal which would have put them into the last 4, but Ronaldo leveled the score on the night with 15 minutes remaining following a Casemiro cross.
Bayern München: Neuer; Lahm, Boateng, Hummels, Alaba; Alonso, Vidal; Robben, Thiago, Ribery; Lewandowski. Bayern were not done as less than a minute later they would answer right back with Thomas Muller and Robert Lewandowski combining to pressure Sergio Ramos into an ill advised back pass that Keylor Navas clearly was not ready for and it slipped in for an own goal.
Be Civil - It's OK to have a difference in opinion but there's no need to be a jerk. "We are not going to worry about that".
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